Arithmetic Grade Four

Lesson Fifty-four: Divisibility

You've probably done count-bys before. Look at some of these examples to get an idea of what we're talking about: 

  Counting by 2's: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

  Counting by 4's: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44

  Counting by 7's: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77
Understanding count-bys should help you to understand divisibility. When we say that a number is divisible by another number, we mean that when we divide one number by the other there will be no remainder. Look at these examples: 

   25 is divisible by 5 because 25 / 5 = 5 (without any remainder).

   27 is not divisible by 5 since when we divide 27 by 5 we get a remainder.

   30 is divisible by 6 because 30 / 6 = 5 (without any remainder).

   41 is not divisible by 6 since when we divide 41 by 6 we get a remainder.
If a number is a count by of another number, it is divisible by the count by number.

For instance: 


  Counting by 8's: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88.

  40 is divisible by 8. We know this by looking at the list of
  count-bys for 8. 

  44 is not divisible by 8. We know this since 44 is not on the
  list of count-bys for 8.
Here are a couple more examples: 

  Is 42 divisible by 7?

  We know two ways of figuring the answer to this problem:

  a) 42 / 7 = 6 (without a remainder), so 42 is divisible by 7.

  b) We can make a list of count-by's for 7:

       7, 14, 21, 28, 35, 42, 49, 56, etc.

  We can see that 42 is on this list and so we know it is divisible by 7.
Now you will try a few of these yourself.

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