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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
Options
2
3
5
10
Solution
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
o 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 can not 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.
Thus the answer is 2.
Hence the correct choice is (a).
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