Finding Common Factors

Objective

Know how to find common factors of two numbers

Example

Is 9 a common factor in the following fraction?

108 ÷ 9 = 12

144 ÷ 9 = 16

Answer: yes

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Explanation

Common Factor

• Common: For both

• Factor: A number we can divide by without a remainder

So, a common factor is a number that can divide into our numerator and denominator without a remainder

To figure out if a number is a factor, you can just try to divide and see if you get a remainder. If you get a remainder, it's not a factor. This can take forever even if you are good at division.

Here are some great shortcuts to help us know if numbers are a factor, without ever having to try to divide!

Is 2 a factor?

If the number in the units place is even (0, 2, 4, 6, or 8), 2 is a factor

304 4 is even, so 2 is a factor of 304

23,303 3 is odd, so 2 is not a factor 23,303

Is 3 a factor?

It's weird, but add up all the digits of the number. If 3 is a factor of that new number, then 3 is a factor of the original number

324 3+2+4 = 9. 3 can divide into 9, so 3 is a factor of 324

23,303 2+3+3+0+3 = 11 (do it again)

1+1 = 2. 3 can not divide into 2, so 3 is not a factor of 23,303

Is 5 a factor?

If the number in the units place is 0 or 5, then 5 is a factor

305 5 is 5, so 5 is a factor of 305

300 0 is 0, so 5 is a factor of 305

23,303 3 is not 0 or 5, so 5 is not a factor of 23,303

Is 5 a factor?

If the number in the units place is 0 or 5, then 5 is a factor

305 5 is 5, so 5 is a factor of 305

300 0 is 0, so 5 is a factor of 305

23,303 3 is not 0 or 5, so 5 is not a factor of 23,303

Is 6 a factor?

If both 2 and 3 are factors, 6 is also a factor

300 2 is a factor of 300, 3 is a factor of 300, so 6 is a factor of 300

23,302 2 is a factor of 23,302, but 3 is not a factor, so 6 is not a factor of 23,302

Is 9 a factor?

It's weird, but add up all the digits of the number. If 9 is a factor of that new number, then 9 is a factor of the original number

324 3+2+4 = 9. 9 can divide into 9, so 9 is a factor of 324

23,303 2+3+3+0+3 = 11 (do it again)

1+1 = 2. 9 can not divide into 2, so 9 is not a factor of 23,303

Is 10 a factor?

If the number in the units place is 0, then 10 is a factor

300 0 is 0, so 10 is a factor of 305

23,303 3 is not 0, so 10 is not a factor of 23,303

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Examples

Example 1

Is 5 a common factor in the following fraction?

• 5 is a factor of 100

• but 5 is not a factor of 94

Answer: no

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Example 2

Is 3 a common factor in the following fraction?

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Ready?