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Number System — formula, example and practice

Divisibility, remainders, LCM/HCF and place-value questions that decide easy marks.

Content type: original worked example. Not labelled as a previous-year question.

Timed GK/quant mock Shortcuts CBSE Class 10 Maths 150 questions

Formula

Dividend = Divisor × Quotient + Remainder

Whole numbers, factors, remainders and divisibility. LCM/HCF is the neighbouring chapter.

What you should learn here

Remainder questions in SSC often hide the form N = LCM×k + R. Write that line first.

Worked example

Question. Smallest number that leaves remainder 1 when divided by 2, 3 and 5?

Solution. LCM(2,3,5)+1 = 31.

Common mistake. Using HCF where the question asks for a common multiple (LCM).

When to use the shortcut. Divisibility rules (2,3,4,5,8,9,11) should be automatic before you open a calculator habit.

Related chapters and tests

Simplification Percentage Ratio and Proportion Profit and Loss All formulas SSC GD mocks SSC CGL mocks

150 important Number System questions

Original arithmetic practice for this page. Not labelled as previous-year SSC/railway items. Tap an option to mark it. Open “Answer” for the working.

Q. 1संख्या

Remainder when 84 is divided by 3 is

Answer / solution

Correct option: C

84 = 3×28 + 0.

Q. 2संख्या

11² equals

Answer / solution

Correct option: A

Square = 121.

Q. 3संख्या

The next even number after 19 is

Answer / solution

Correct option: B

Next even = 20.

Q. 4संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 5संख्या

Unit digit of 16 × 22 is

Answer / solution

Correct option: D

Product = 352; unit digit 2.

Q. 6संख्या

Remainder when 144 is divided by 4 is

Answer / solution

Correct option: D

144 = 4×36 + 0.

Q. 7संख्या

16² equals

Answer / solution

Correct option: D

Square = 256.

Q. 8संख्या

The next even number after 29 is

Answer / solution

Correct option: B

Next even = 30.

Q. 9संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 10संख्या

Unit digit of 13 × 21 is

Answer / solution

Correct option: B

Product = 273; unit digit 3.

Q. 11संख्या

Remainder when 96 is divided by 5 is

Answer / solution

Correct option: A

96 = 5×19 + 1.

Q. 12संख्या

21² equals

Answer / solution

Correct option: D

Square = 441.

Q. 13संख्या

The next even number after 39 is

Answer / solution

Correct option: B

Next even = 40.

Q. 14संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 15संख्या

Unit digit of 18 × 20 is

Answer / solution

Correct option: D

Product = 360; unit digit 0.

Q. 16संख्या

Remainder when 156 is divided by 6 is

Answer / solution

Correct option: A

156 = 6×26 + 0.

Q. 17संख्या

26² equals

Answer / solution

Correct option: A

Square = 676.

Q. 18संख्या

The next even number after 49 is

Answer / solution

Correct option: B

Next even = 50.

Q. 19संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 20संख्या

Unit digit of 15 × 19 is

Answer / solution

Correct option: B

Product = 285; unit digit 5.

Q. 21संख्या

Remainder when 108 is divided by 3 is

Answer / solution

Correct option: A

108 = 3×36 + 0.

Q. 22संख्या

31² equals

Answer / solution

Correct option: D

Square = 961.

Q. 23संख्या

The next even number after 19 is

Answer / solution

Correct option: B

Next even = 20.

Q. 24संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 25संख्या

Unit digit of 12 × 18 is

Answer / solution

Correct option: B

Product = 216; unit digit 6.

Q. 26संख्या

Remainder when 168 is divided by 4 is

Answer / solution

Correct option: B

168 = 4×42 + 0.

Q. 27संख्या

36² equals

Answer / solution

Correct option: A

Square = 1296.

Q. 28संख्या

The next even number after 29 is

Answer / solution

Correct option: B

Next even = 30.

Q. 29संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 30संख्या

Unit digit of 17 × 23 is

Answer / solution

Correct option: C

Product = 391; unit digit 1.

Q. 31संख्या

Remainder when 120 is divided by 5 is

Answer / solution

Correct option: B

120 = 5×24 + 0.

Q. 32संख्या

41² equals

Answer / solution

Correct option: C

Square = 1681.

Q. 33संख्या

The next even number after 39 is

Answer / solution

Correct option: B

Next even = 40.

Q. 34संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 35संख्या

Unit digit of 14 × 22 is

Answer / solution

Correct option: A

Product = 308; unit digit 8.

Q. 36संख्या

Remainder when 180 is divided by 6 is

Answer / solution

Correct option: C

180 = 6×30 + 0.

Q. 37संख्या

46² equals

Answer / solution

Correct option: B

Square = 2116.

Q. 38संख्या

The next even number after 49 is

Answer / solution

Correct option: B

Next even = 50.

Q. 39संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 40संख्या

Unit digit of 19 × 21 is

Answer / solution

Correct option: C

Product = 399; unit digit 9.

Q. 41संख्या

Remainder when 132 is divided by 3 is

Answer / solution

Correct option: D

132 = 3×44 + 0.

Q. 42संख्या

11² equals

Answer / solution

Correct option: A

Square = 121.

Q. 43संख्या

The next even number after 19 is

Answer / solution

Correct option: B

Next even = 20.

Q. 44संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 45संख्या

Unit digit of 16 × 20 is

Answer / solution

Correct option: C

Product = 320; unit digit 0.

Q. 46संख्या

Remainder when 84 is divided by 4 is

Answer / solution

Correct option: B

84 = 4×21 + 0.

Q. 47संख्या

16² equals

Answer / solution

Correct option: D

Square = 256.

Q. 48संख्या

The next even number after 29 is

Answer / solution

Correct option: B

Next even = 30.

Q. 49संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 50संख्या

Unit digit of 13 × 19 is

Answer / solution

Correct option: A

Product = 247; unit digit 7.

Q. 51संख्या

Remainder when 144 is divided by 5 is

Answer / solution

Correct option: A

144 = 5×28 + 4.

Q. 52संख्या

21² equals

Answer / solution

Correct option: D

Square = 441.

Q. 53संख्या

The next even number after 39 is

Answer / solution

Correct option: B

Next even = 40.

Q. 54संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 55संख्या

Unit digit of 18 × 18 is

Answer / solution

Correct option: C

Product = 324; unit digit 4.

Q. 56संख्या

Remainder when 96 is divided by 6 is

Answer / solution

Correct option: C

96 = 6×16 + 0.

Q. 57संख्या

26² equals

Answer / solution

Correct option: A

Square = 676.

Q. 58संख्या

The next even number after 49 is

Answer / solution

Correct option: B

Next even = 50.

Q. 59संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 60संख्या

Unit digit of 15 × 23 is

Answer / solution

Correct option: B

Product = 345; unit digit 5.

Q. 61संख्या

Remainder when 156 is divided by 3 is

Answer / solution

Correct option: C

156 = 3×52 + 0.

Q. 62संख्या

31² equals

Answer / solution

Correct option: D

Square = 961.

Q. 63संख्या

The next even number after 19 is

Answer / solution

Correct option: B

Next even = 20.

Q. 64संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 65संख्या

Unit digit of 12 × 22 is

Answer / solution

Correct option: B

Product = 264; unit digit 4.

Q. 66संख्या

Remainder when 108 is divided by 4 is

Answer / solution

Correct option: D

108 = 4×27 + 0.

Q. 67संख्या

36² equals

Answer / solution

Correct option: A

Square = 1296.

Q. 68संख्या

The next even number after 29 is

Answer / solution

Correct option: B

Next even = 30.

Q. 69संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 70संख्या

Unit digit of 17 × 21 is

Answer / solution

Correct option: D

Product = 357; unit digit 7.

Q. 71संख्या

Remainder when 168 is divided by 5 is

Answer / solution

Correct option: C

168 = 5×33 + 3.

Q. 72संख्या

41² equals

Answer / solution

Correct option: C

Square = 1681.

Q. 73संख्या

The next even number after 39 is

Answer / solution

Correct option: B

Next even = 40.

Q. 74संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 75संख्या

Unit digit of 14 × 20 is

Answer / solution

Correct option: B

Product = 280; unit digit 0.

Q. 76संख्या

Remainder when 120 is divided by 6 is

Answer / solution

Correct option: D

120 = 6×20 + 0.

Q. 77संख्या

46² equals

Answer / solution

Correct option: B

Square = 2116.

Q. 78संख्या

The next even number after 49 is

Answer / solution

Correct option: B

Next even = 50.

Q. 79संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 80संख्या

Unit digit of 19 × 19 is

Answer / solution

Correct option: D

Product = 361; unit digit 1.

Q. 81संख्या

Remainder when 180 is divided by 3 is

Answer / solution

Correct option: A

180 = 3×60 + 0.

Q. 82संख्या

11² equals

Answer / solution

Correct option: A

Square = 121.

Q. 83संख्या

The next even number after 19 is

Answer / solution

Correct option: B

Next even = 20.

Q. 84संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 85संख्या

Unit digit of 16 × 18 is

Answer / solution

Correct option: D

Product = 288; unit digit 8.

Q. 86संख्या

Remainder when 132 is divided by 4 is

Answer / solution

Correct option: A

132 = 4×33 + 0.

Q. 87संख्या

16² equals

Answer / solution

Correct option: D

Square = 256.

Q. 88संख्या

The next even number after 29 is

Answer / solution

Correct option: B

Next even = 30.

Q. 89संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 90संख्या

Unit digit of 13 × 23 is

Answer / solution

Correct option: A

Product = 299; unit digit 9.

Q. 91संख्या

Remainder when 84 is divided by 5 is

Answer / solution

Correct option: C

84 = 5×16 + 4.

Q. 92संख्या

21² equals

Answer / solution

Correct option: D

Square = 441.

Q. 93संख्या

The next even number after 39 is

Answer / solution

Correct option: B

Next even = 40.

Q. 94संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 95संख्या

Unit digit of 18 × 22 is

Answer / solution

Correct option: C

Product = 396; unit digit 6.

Q. 96संख्या

Remainder when 144 is divided by 6 is

Answer / solution

Correct option: C

144 = 6×24 + 0.

Q. 97संख्या

26² equals

Answer / solution

Correct option: A

Square = 676.

Q. 98संख्या

The next even number after 49 is

Answer / solution

Correct option: B

Next even = 50.

Q. 99संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 100संख्या

Unit digit of 15 × 21 is

Answer / solution

Correct option: A

Product = 315; unit digit 5.

Q. 101संख्या

Remainder when 96 is divided by 3 is

Answer / solution

Correct option: A

96 = 3×32 + 0.

Q. 102संख्या

31² equals

Answer / solution

Correct option: D

Square = 961.

Q. 103संख्या

The next even number after 19 is

Answer / solution

Correct option: B

Next even = 20.

Q. 104संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 105संख्या

Unit digit of 12 × 20 is

Answer / solution

Correct option: A

Product = 240; unit digit 0.

Q. 106संख्या

Remainder when 156 is divided by 4 is

Answer / solution

Correct option: B

156 = 4×39 + 0.

Q. 107संख्या

36² equals

Answer / solution

Correct option: A

Square = 1296.

Q. 108संख्या

The next even number after 29 is

Answer / solution

Correct option: B

Next even = 30.

Q. 109संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 110संख्या

Unit digit of 17 × 19 is

Answer / solution

Correct option: C

Product = 323; unit digit 3.

Q. 111संख्या

Remainder when 108 is divided by 5 is

Answer / solution

Correct option: A

108 = 5×21 + 3.

Q. 112संख्या

41² equals

Answer / solution

Correct option: C

Square = 1681.

Q. 113संख्या

The next even number after 39 is

Answer / solution

Correct option: B

Next even = 40.

Q. 114संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 115संख्या

Unit digit of 14 × 18 is

Answer / solution

Correct option: A

Product = 252; unit digit 2.

Q. 116संख्या

Remainder when 168 is divided by 6 is

Answer / solution

Correct option: A

168 = 6×28 + 0.

Q. 117संख्या

46² equals

Answer / solution

Correct option: B

Square = 2116.

Q. 118संख्या

The next even number after 49 is

Answer / solution

Correct option: B

Next even = 50.

Q. 119संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 120संख्या

Unit digit of 19 × 23 is

Answer / solution

Correct option: D

Product = 437; unit digit 7.

Q. 121संख्या

Remainder when 120 is divided by 3 is

Answer / solution

Correct option: B

120 = 3×40 + 0.

Q. 122संख्या

11² equals

Answer / solution

Correct option: A

Square = 121.

Q. 123संख्या

The next even number after 19 is

Answer / solution

Correct option: B

Next even = 20.

Q. 124संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 125संख्या

Unit digit of 16 × 22 is

Answer / solution

Correct option: D

Product = 352; unit digit 2.

Q. 126संख्या

Remainder when 180 is divided by 4 is

Answer / solution

Correct option: D

180 = 4×45 + 0.

Q. 127संख्या

16² equals

Answer / solution

Correct option: D

Square = 256.

Q. 128संख्या

The next even number after 29 is

Answer / solution

Correct option: B

Next even = 30.

Q. 129संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 130संख्या

Unit digit of 13 × 21 is

Answer / solution

Correct option: B

Product = 273; unit digit 3.

Q. 131संख्या

Remainder when 132 is divided by 5 is

Answer / solution

Correct option: D

132 = 5×26 + 2.

Q. 132संख्या

21² equals

Answer / solution

Correct option: D

Square = 441.

Q. 133संख्या

The next even number after 39 is

Answer / solution

Correct option: B

Next even = 40.

Q. 134संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 135संख्या

Unit digit of 18 × 20 is

Answer / solution

Correct option: D

Product = 360; unit digit 0.

Q. 136संख्या

Remainder when 84 is divided by 6 is

Answer / solution

Correct option: A

84 = 6×14 + 0.

Q. 137संख्या

26² equals

Answer / solution

Correct option: A

Square = 676.

Q. 138संख्या

The next even number after 49 is

Answer / solution

Correct option: B

Next even = 50.

Q. 139संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 140संख्या

Unit digit of 15 × 19 is

Answer / solution

Correct option: B

Product = 285; unit digit 5.

Q. 141संख्या

Remainder when 144 is divided by 3 is

Answer / solution

Correct option: A

144 = 3×48 + 0.

Q. 142संख्या

31² equals

Answer / solution

Correct option: D

Square = 961.

Q. 143संख्या

The next even number after 19 is

Answer / solution

Correct option: B

Next even = 20.

Q. 144संख्या

33 mod 3 is

Answer / solution

Correct option: A

Remainder = 0.

Q. 145संख्या

Unit digit of 12 × 18 is

Answer / solution

Correct option: B

Product = 216; unit digit 6.

Q. 146संख्या

Remainder when 96 is divided by 4 is

Answer / solution

Correct option: D

96 = 4×24 + 0.

Q. 147संख्या

36² equals

Answer / solution

Correct option: A

Square = 1296.

Q. 148संख्या

The next even number after 29 is

Answer / solution

Correct option: B

Next even = 30.

Q. 149संख्या

63 mod 3 is

Answer / solution

Correct option: C

Remainder = 0.

Q. 150संख्या

Unit digit of 17 × 23 is

Answer / solution

Correct option: C

Product = 391; unit digit 1.

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