Question

if a number is a factor of each of the two given numbers, then it must be a factor of their sum.

Answer 1

yes I agree with the given statement that if any number is a factor of the given 2 numbers then it will be the factor of their sum.

example :
7 is the factor of 14 and even 21
⇒ sum of 14 and 21 is 35
∴ The 35 is the factor 7

⇒ yeah I agree with the given statement that any number which is a factor of the given 2 numbers is a factor of the sum of it also.

Answer 2

yes.
ex-
5 is a factor of 15 and 20
5 is also factor of 15+20 = 35

so, this statement if true.