Question

If the least prime factors of two positive integers a and b are 5 and 13 respectively, then the least prime factor of a + b, is _________.

Answer 1

It is given that the least prime factors of two positive integers a and b are 5 and 13 respectively.

Thus, a = 5p and b = 13q , where p and q are some natural numbers.

Now, a + b = 5p + 13q

Since, 5p and 13q both are odd numbers
and sum of two odd numbers is even.

Therefore, a + b is an even number.

Hence, the least prime factor of a + b, is 2 .