Question

given that 24 is factor of 120 and 408 show that 24 is factor of the sum of 120 and 408

Answer 1

24 is a factor of 120. Thus 120 can be expressed as 24x. Also, 24 is a factor of 408, thus 408 can be expressed as 24y.

So, 120+408=24x+24y. Now, we can factorise as follows-

24(x+y). We know that x is a natural number (as it is a factor) and so is y. So x+y will also be a natural number. (this was important because if x+y was a fraction, we wouldn't have been able to prove).

If we divide 24(x+y) by 24, we get the quotient x+y, which is a natural number, and no remainder, thus 24 is a factor of 24(x+y). But 24(x+y) was 120+408. Thus 24 is also a factor of 120+408.