Question

If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a + b, is ______.

पर्याय

• 2

• 3

• 5

• 10

Answer 1

If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a + b, is 2.

Explanation:

Since `7+3=10`

The least prime factor of  a + b has to be 2; unless a + b is a prime number greater than 2.

Suppose a +b is a prime number greater than 2. Then a + b must be an odd number

o one of a or b must be an even number. 

Suppose then that a is even. Then the least prime factor of a is 2; which is not 3 or 7. So a can not be an even number nor can b be an even number. Hence a + b can not be a prime number greater than 2 if the least prime factor of a is 3 and b is 7.

Thus the answer is 2.

Hence the correct choice is (a).