Question

If 3 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
A. 2
B. 3
C. 5
D. 10

Answer 1

Answer:

Step-by-step explanation:

Since 7+3=10. The least prime factor of a+b has to be 2; unless a+b is a prime number greater than 2.

Suppose a+b is a prime number greater than 2. Then a+b must be an odd number. So one of a or b must be an even number. Suppose then that a is even. Then the least prime factor of a is 2; which is not 3 or 7. So a cannot be an even number. Nor can b be an even number. Hence a+b can not be a prime number greater than 2 if the least prime factor of a is 3 and b is 7.

Hence the answer is 2.

Answer 2

Among the given options option (a) 2 is correct.

Step-by-step explanation:

Given :  

Least prime factor of ‘a’ is 3 and least prime factor of ‘b’ is 7.

sum of least prime factors of a and b = (a + b) = 3 + 7 = 10

(a + b) = 10

Least factor of 10 is 2

Hence, the least factor of (a + b) is also 2.

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