Question

a and b are two +ve integers such thar a > b . If 3 is the least prime factor of a and 7 is the least prime factor of b , what will be the least Prime factor of (i) a + b (ii) a – b (iii) ab

Answer 1

Answer:

When 3 is the least Prime Factor of some (a) Number, obviously 2 is not a factor of such a Number and thus we can conclude that the Number is odd. So we can say that a = 2n+1 for some n.

Similarly when 7 is the least Prime Factor of another (b) Number, obviously 2 is not not a factor of that Number and again we can conclude that that Number also is odd. So we can say that b = 2k - 1 for some k.

Adding a +b gives:

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

a + b = 2(n+k)

It is immaterial what the real values of n and k are, we can see 2 as a factor there. And thus the least Prime Factor of (a+b) is clearly 2!

So 2 is the required answer.