prove in two different ways that 2 divides 114

Question

a. prove in two different ways that 2 divides 114.

b. prove in two different ways that 3 | 336.

Answer 1

a.  since 114 is even, we know that 2 will divide into it without remainder

b.  since the sum of the digits of 336 (sum = 12) is itself a multiple of 3, we understand that 3 will divide into it without remainder.

 

a. we can factor 114 = 2 × 57, so division by 2 will cancel the 2 factor, leaving quotient 57 w/o remainder

b. we can factor 336 = 3 × 112, so division by 3 will cancel the 3 factor, leaving quotient 112 w/o remainder.