Factors are numbers that are multiplied to get a product.
A factor pair is a set of two numbers multiplied together to make a product.
For example, a factor pair for 6 is:
2 and 3
2 × 3 = 6 ✅
Some products, or numbers, have many factor pairs.
The number 12 has 3 factor pairs.
1 and 12
2 and 6
3 and 4
Prime numbers have only one factor pair, themselves and the number 1.
For example, the prime number 5 has just one factor pair:
1 and 5
The first 10 prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
To find every factor pair for a number, try dividing it by every number from 1 up to that number.
The numbers that divide it evenly, without remainder, are the factors.
For example, to find the factor pairs for 12, we start by dividing 12 by 1.
12 ÷ 1 = 12
The number itself and 1 are a factor pair of any number.
Then, move on to 2.
12 ÷ 2 = 6
2 divides 12 without remainder, so 2 and 6 are also factor pairs. ✅
Next, we check if 3 is a factor.
12 ÷ 3 = 4
Yes, there's no remainder. It's another factor pair. ✅
12 ÷ 4 = 3
Oh, wait. We already found that 3 and 4 are factors.
That means there are no more factors left to try. We found all of them.
The factor pairs of 12 are:
1 and 12
2 and 6
3 and 4
What are the factor pairs for 36?
Let's start by dividing 36 by 1.
36 ÷ 1 = 36
We found the first factor pair of 36: 1 and 36. ✅
Then continue dividing 36 by 2.
36 ÷ 2 = 18
2 divides 36 evenly, without remainder, so 2 and 18 are factors pairs too. ✅
Use long division to figure this out if you need:
Next, divide 36 by 3.
36 ÷ 3 = 12
There's no remainder! We found another factor pair. ✅
Continue dividing by 4.
36 ÷ 4 = 9
We found another factor pair. ✅
Can we divide 36 by 5 evenly?
"Evenly" means we can divide a number with no remainder.
36 ÷ 5 = ?
Let's see....
There is a remainder. So 5 is not a factor of 36.
Let's keep going. The next number to check is 6.
36 ÷ 6 = ?
There's no remainder. That means 6 is a factor of 36. ✅
Does 36 have any other factors?
Nope. Now, let's list all the factor pairs of 36.
1 and 36
2 and 18
3 and 12
4 and 9
6 and 6
Great job learning about factor pairs.
Now, let's try the practice.