Question

find the smallest prime number dividing the sum 3 ^11 5^13

Answer 1

3^11 and 5^13 are the product of odd numbers and the number will be odd 
the sum of 3^11 and 5^13 is sum of odd numbers and the number will be even
the smallest prime number that divides the sum is 2

Answer 2

Answer:

Smallest prime number that divides the sum of $3^{11} \text { and } 5^{13}$is 2.

Solution:

Product of odd numbers will be odd.

That is $3^{11} \times 5^{13}=177147 \times 1220703125=\text { an odd number }$

Sum of odd numbers will be even.

That is, $3^{11}+5^{13}=177147+1220703125=1220880272=\text { an even number }$

Every even number can be divided by only even prime number 2.

Therefore, smallest prime number that divides the sum of $3^{11} \text { and } 5^{13}$ is 2.