Factor Rainbows
Factors are numbers that, when multiplied, equal a product. In other words, in a multiplication problem, the numbers that are being multiplied together are the factors.
Creating factor rainbows is an easy way to identify all of the factors for a given number (or product).
When finding the factors of a number, there are 2 strategies you can use.
STRATEGY 1:
First, you could start with 1 and multiply it with a number that equals the factor. Then go to 2, 3, 4, and so on. For example:
Find all factors for the number 16:
1 x 16 = 16
2 x 8 = 16
3 x X =16 <---there are no whole number that when multiplied by 3 will equal 16
4 x 4 = 16
STOP! Once we find a factor that is multiplied by itself to get the product, we don't need to go any further, we would only find numbers that we have already identified as factors.
Now, we need to list all of the factors for 16 in order from LEAST to GREATEST. When writing the factors on paper, you connect the factor pairs with large arches, which will look like a rainbow. When listing a factor that is multiplied by itself, you only need to write the number once.
1, 2, 3, 4, 8, 16
STRATEGY 2:
Instead multiplying up, you could divide the product starting with 1 then continuing on to 2, 3, 4, and so on.
Find all factors for 2
16/1 = 16
16/2 =
16/3 = X <---16/3=5.3333 which is not a whole number.
16/4 = 4
Again, we need to list all of the factors for 16 in order from LEAST to GREATEST. When writing the factors on paper, you connect the factor pairs with large arches, which will look like a rainbow. When listing a factor that is multiplied by itself, you only need to write the number once.
1, 2, 3, 4, 8, 16
Creating factor rainbows is an easy way to identify all of the factors for a given number (or product).
When finding the factors of a number, there are 2 strategies you can use.
STRATEGY 1:
First, you could start with 1 and multiply it with a number that equals the factor. Then go to 2, 3, 4, and so on. For example:
Find all factors for the number 16:
1 x 16 = 16
2 x 8 = 16
3 x X =16 <---there are no whole number that when multiplied by 3 will equal 16
4 x 4 = 16
STOP! Once we find a factor that is multiplied by itself to get the product, we don't need to go any further, we would only find numbers that we have already identified as factors.
Now, we need to list all of the factors for 16 in order from LEAST to GREATEST. When writing the factors on paper, you connect the factor pairs with large arches, which will look like a rainbow. When listing a factor that is multiplied by itself, you only need to write the number once.
1, 2, 3, 4, 8, 16
STRATEGY 2:
Instead multiplying up, you could divide the product starting with 1 then continuing on to 2, 3, 4, and so on.
Find all factors for 2
16/1 = 16
16/2 =
16/3 = X <---16/3=5.3333 which is not a whole number.
16/4 = 4
Again, we need to list all of the factors for 16 in order from LEAST to GREATEST. When writing the factors on paper, you connect the factor pairs with large arches, which will look like a rainbow. When listing a factor that is multiplied by itself, you only need to write the number once.
1, 2, 3, 4, 8, 16
