Factorization

[anusha.bondili]

The integer m is a multiple of 154, 250, and 264. Which of the following do NOT have to be factors of m?Indicate all possible values :

a. 176
b. 242
c. 275
d. 924
e. 2,500
f. 7,000

Thanks in advance.

[tommywallach]

Hey Anusha,

The integer m is a multiple of 154, 250, and 264. Which of the following do NOT have to be factors of m?Indicate all possible values :

All you have to do for this primes and divisibility question is find the primes of m:

154 --> 2 * 11 * 7
250 --> 5 * 5 * 5 * 2
264 --> 2 * 2 * 2 * 3 * 11

Then, by the rules of divisibility, we know that the smallest value of m would be --> 2 * 2 * 2 * 3 * 5 * 5 * 5 * 7 * 11 = 231,000

So m is definitively a multiple of 231,000. Now we just divide that by all the possibilities in the answer choices and whichever ones come out to be integers are the ones we should pick:

a. 231,000/176 = no
b. 231,000/242 = no
c. 231,000/275 = yes
d. 231,000/924 = yes
e. 231,000/2,500 = no
f. 231,000/7,000 =yes

Hope that helps!

-t