Question

State if the given statement is True or False.

80 is a factor of r, then 15 is also a factor of r.

• A. True
• B. False

Answer 1

Answer: (B)

If r is divisible by 80, its prime factors include 2,2,2,2, and 5, as indicated by the prime box to the left. Therefore, any integer that can be constructed as a product of any of these prime factors is also a factor of r. Factoring 15, you get 3 $\times$ 5. Since you don't know whether the prime factor 3 is in the prime box, you cannot determine whether 15 is a factor of r. As numerical examples, you could take r = 80, in which case 15 is not a factor of r, or r = 240, in which case 15 is a factor of r.