Example 5

Example 5

Consider the following conjecture:

• If the last digit of a Whole Number is divisible by 2, then the entire number is divisible by 2.

1. Give two examples showing the conjecture works.
   
   58 ends in 8, which is divisible by 2, and 58 ÷ 2 = 29, so 58 is divisible by 2.
   
   292 ends in 2, which is divisible by 2, and 292 ÷ 2 = 146, so 292 is divisible by 2.
   
   
2. Prove the conjecture.
   
   Since you proved it already (in Example 4), you can use the fact that
   
   'if is an Integer and is an Integer, then is also an Integer' to help with this proof.
   
   Any Whole Number can be rewritten in the form b + c, where c is the ones value in the given Whole Number. The b value has a zero in the ones place and so is always divisible by 10. Since 2 is a factor of 10, 2 is also a factor of b. This means that if c, the ones value, is divisible by a = 2, then b + c will also be divisible by 2.