What is a Factor?
One of two or more quantities that divides a given quantity without a remainder. One of the numbers that make up a number by multiplication.
A factor is a number that divides another number evenly, with no remainder. In multiplication, a factor is also one of the numbers you multiply together to get a product.
For example: 3 × 4 = 12
In this case, 3 and 4 are factors of 12, because:
- They multiply together to make 12
- They both divide evenly into 12
That means:
- 3 × 4 = 12, so 3 and 4 are factors
- 12 ÷ 3 = 4 and 12 ÷ 4 = 3, so 12 can be divided by both 3 and 4 with no remainder
Other factors of 12 include 1, 2, 6, and 12. These are all numbers that divide evenly into 12.
You can also say that when two or more numbers are multiplied together, each number is a factor of the product.
Understanding factors helps with:
- Finding greatest common factors (GCF)
- Reducing fractions
- Working with multiples and divisibility
- Building fluency with multiplication and division facts
When Do Students Learn About Factors?
Students are introduced to factors when they begin working with multiplication and division facts, and they explore them more deeply as they learn about number relationships.
Grades 3–5 – Introduction to Factors
Students learn what it means for a number to be a factor, how to identify all the factors of a number, and how to use factors in multiplication, division, and simplifying fractions.
Grades 6+ – Factors in Advanced Topics
Students use factors in prime factorization, greatest common factor (GCF), least common multiple (LCM), and algebraic expressions.
