Smallest Prime Factors

The smallest prime factor of a positive integer W W is 11.
The smallest prime factor of another positive integer K K is 31.
What is the smallest prime factor of K + W K+W ?

2 3 11 31

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2 solutions

Anandmay Patel
Jul 30, 2016

Relevant wiki: Even and Odd Numbers

W's least prime factor is 11 means all its rest prime divisors are greater than 11(and 2 obviously) so all are odd.Same for K.
ODD x ODD=ODD
and
ODD + ODD=EVEN
So by this,K and W are odds ,and their sum(K+W) is even,so divisible by 2,i.e.,its least prime divisor.

Manisha Gupta
Aug 7, 2016

I took the numbers as 11 and 31 Added them 11+ 31 = 42 Least prime divisor of 42 = 2

Good use of experimentation.

Anandmay Patel - 4 years, 10 months ago

Specifically its 11 square plus 31 square

Haziq Sheikh - 4 years, 4 months ago

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