Question

If least prime factor of "a" is 3 and least prime factor of "b" is 7, the least prime factor of (a + b) ?

Answer 1

least prime factor of "a" is 3 and least prime factor of "b" is 7
so sum of least prime factors of a and b = 3+7 = 10
and least factor of 10 is 2
so least factor of a + b is also 2

Answer 2

Answer:

2

Step-by-step explanation:

When 3 will be the least prime factor of some a number, then 2 will not be a factor of such a number and thus it can be concluded that the number is odd. Thus, a = 2n+1 for some n.

Similarly when 7 will be the least prime factor of another b number, then again 2 will not be a factor of that number and it can be concluded that that number also is odd. Thus b = 2k - 1 for some k.

Adding a +b -

= a + b = 2n + 1 + 2k -1

= a + b = 2 (n+k)

It can not be figured out as to what are the real values of n and k are, and only 2 can be observed as a factor there. Thus, the least prime factor of (a+b) will be clearly 2.

Hence a + b is even (i.e a multiple of 2). Thus the least prime factor of 'a + b' is 2.