Question

If a and b are two positive integers such that the least prime factor of a is 3 and that of b is 5. What is the least prime factors of a+b

Answer 1

Hey

Here is your answer,

Given that, a is a positive integer and 3 is least prime factor of a.

Also, b is a positive integer and 5 is least prime factor of b.

Since least prime factor of a is 3, it implies that 'a' is an odd number

∵ if a is even then 2 is least prime factor of a.

Similarly b is also an odd number.

Now, it is known that sum of two odd numbers is an even number.

Hence, a + b will be an even number.

∴ The least prime factor of a + b is 2

Hope it helps you!

Answer 2

a=3 and b=5
a+b=8
2*2*2=8
Therefore, 2 is the least prime factor of a+b