Question

All numbers divisible by 22 and 24 are also divisible by which of the following?

221
132
204
250
154

Answer 1

if P is divisible by both 22 and 24 we can write:

\[P = (22)(24)x \]

so can we make any of the numbers in your list out of the factors of both 22 and 24?

well 22 = 11 x 2 and 24 = 2 x 3 x 2 x 2

so we can make 132 by doing 11 x 3 x 2 x 2

Answer 2

132 is the answer

Answer 3

one possible way to answer is to work out the prime factorisation of each of those numbers. 22 has prime factorization: 22=2*11. 24 has prime factorization: 24=2*2*2*3. So all numbers that are divisible by 22 have the prime factors 2*11 somewhere within them... all numbers divisible by 24 have the prime factors 2*2*2*3... so if a number is divisible by both, then it has prime factors 2*2*2*3*11... so work out the prime factorizations of 221, 132, etc... and whichever of those has 2*2*2*3*11 also divides those numbers...