Arithmetic Grade Five

Lesson Eighty-three: Factoring

Finding the greatest factor of odd numbers is not as easy as finding the largest factor of even numbers. This is because we can't just automatically divide by two like we can with even numbers. Here's an example using an odd number. 

    FACTORS of 21: 1, 3, 7, 21.

    GREATEST FACTOR OF 21: 7.
Here's another example using a different odd number. 

    FACTORS of 35: 1, 5, 7, 35.

    GREATEST FACTOR OF 35: 7.
There are two strategies you can use to find the largest factor of odd numbers:
  1. List all the factors of the number and select the largest one
  2. Start dividing by 3, then try 5, then try 7, and keep on trying prime numbers until you have tried the prime numbers which are less than half of your number
The example shown above show the listing method. Here's an example using the dividing by primes method: 

     Find the greatest factor of 49.

     Try these numbers:
     1) Try 3. 49 is not divisible by 3.
     2) Try 5. 49 is not divisible by 5.
     3) Try 7. YES!

     49 / 7 = 7

     Therefore, 7 is the greatest factor of 49.
In the next practice exercise you will be asked to identify the largest factor of each number.

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