Question

If the least prime fator of a is 3 and least prime factor of b is 7 thdm least prime factor of (a+b) is 2 .Justify.​

Answer 1

Answer:

Step-by-step explanation:

example for it..

Prime factors of 100: 2, 2, 5, 5

100 =  2 × 2 × 5 × 5

=  22 × 52

Factor tree:

100

| \  

50   2

| \  

25   2

| \  

5   5

Answer 2

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Question: If the least prime fator of a is 3 and least prime factor of b is 7 thm least prime factor of (a+b) is 2 .Justify.​

Answer: 2

Solution:

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.

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