Question

The least prime factor of a is 3 and the least prime factor of b is 7. Find the least prime factor of (a + b) giving reasons.
Class 10 Maths

Answer 1

Answer:

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.