Question

If 3 is 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

Answer 1

Since 3 is least prime factor of a and 7 is least prime factor of b, hence none of them is divisible by 2 ( otherwise there least prime factor would have been 2 ).

Hence, we can conclude that both a and b are odd numbers.

Now, 'a' could be written as (2x+1) for x being any positive integer.

[NOTE : any odd nuber is written in this format, for even number we write it as 2x]

Similarly 'b' can be written as (2y+1) for y being any positive integer.

==> a+b = 2x+1+2y+1=2x+2y+2

==> a+b = 2(x+y+1)

So (a+b) is divisible by 2, also 2 is the smallest prime number.

Hence the least prime factor of (a+b) would be 2.