


Last updated at July 9, 2025 by Teachoo
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Using prime factorisation to check if one number is divisible by anotherWe can say that if one number is divisible by another, the prime factorisation of the second number is included in the prime factorisation of the first number Example: Is 168 divisible by 12? Finding prime factorisations of both Therefore, 168 = 2 × 2 × 2 × 3 × 7 12 = 2 × 2 × 3 Now, we can write 168 = (2 × 2 × 3) × 2 × 7 168 = 12 × 2 × 7 Thus, 168 is divisible by 12 Is 75 divisible by 21? Finding prime factorisations of both Therefore, 75 = 3 × 5 × 5 21 = 3 × 7 Since 7 is not there in 75, Thus, 75 is not divisible by 21 Is 42 divisible by 12? Finding prime factorisations of both Therefore, 42 = 2 × 3 × 7 12 = 2 × 2 × 3 Now, (2 × 3) is in 42, but not (2 × 2 × 3) – an extra 2 is missing Thus, 42 is not divisible by 12