Question

State whether True or False.

j is divisible by 12 and 10, then j divisible by 24.

• A. True
• B. False

Answer 1

The correct option is B False

If j is divisible by 12 and by 10, its prime factors include 2, 2, 3, and 5,

What is the minimum number of 2's necessary to create 12 or 10 ? You need two 2's to create 12. You could use one of those same 2's to create the 10. Therefore, there are only two 2's that are definitely in the prime factorization of j, because the 2 in the prime factorization of 10 may be redundant that is, it may be the same 2 as one of the 2's in the prime factorization of 12.

Factoring 24, you get 2 $\times$ 2 $\times$ 2 $\times$ 3. The prime box of j contains at least two 2's and could contain more. The number 24 requires three 2's. Therefore, you may or may not be able to create 24. Thus, 24 is not necessarily a factor of j.