Use Euclid’s algorithm to find HCF(405, 252) and write 405 and 252 as products of primes.
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405 = 252 × 1 + 153
252 = 153 × 1 + 99
153 = 99 × 1 + 54
99 = 54 × 1 + 45
54 = 45 × 1 + 9
45 = 9 × 5 + 0
HCF = 9.
405 = 5 × 3⁴; 252 = 2² × 3² × 7. Common primes give 3² = 9.
Prime factorisation is a check, not a replacement, for the lemma method in exams.
