Natural numbers

Question

The numbers 840 and 876 are divisible by 6. Without actual division can you show the  1716 is also divisible by 6?

Answer 1

If two numbers are both divisible by 6, then their sum or difference is divisible by 6.

840+876=1716 which is divisible by 6

Answer 2

Since 840 is divisible by 6, 840 = 6k, for some positive integer, k.

 

Similarly, 876 = 6m, for some positive integer, m.

 

Since m and k are positive integers, so is m+k

 

1716 = 840+876 = 6k + 6m = 6(k+m)

 

Therefore, 1716 is divisible by 6.