Number Properties : Hard Practice Question # 18 p.200

[nickiss20002000]

The question states that x^2 is a multiple of both 40 and 75. x has three distinct prime factors , and we are looking for what could be the value of x. I am not understanding why x has to have at least two 2's, I thought because 40 = 2*2*2*5, x should have only one 2 in its prime factorization.

[tommywallach]

Hey Nic,

If a number is a multiple of some other number, it has ALL of the prime factors. So any multiple of 40 has 2, 2, 2, and 5 in its primes. So not just two 2s, but three 2s.

-t