What is the greatest common factor (GCF)?
The greatest common factor is the largest whole number that divides each of your numbers exactly, with nothing left over. It is also called the greatest common divisor (GCD), which is what Excel calls it. Finding it is part of grade 6 maths in the Common Core standards.
Source Microsoft Support · GCD function (greatest common divisor), with examples ↗Common Core State Standards · Grade 6, The Number System (6.NS.B.4) ↗
How to calculate the GCF
The quickest way works for numbers of any size: Euclid’s algorithm, which is just repeated division.
Here it is with your numbers:
- 18 = 1 × 12 + 6
- 12 = 2 × 6 + 0
It means 6 is the biggest number that goes into 12 and 18 with nothing left over.
Source NIST · Dictionary of Algorithms and Data Structures: Euclid's algorithm ↗
Factors of each number
For smaller numbers you can also list every factor of each number and pick the biggest one they share.
| Number | Factors (common ones in bold) |
|---|---|
| 12 | 1, 2, 3, 4, 6, 12 |
| 18 | 1, 2, 3, 6, 9, 18 |
GCF examples
FAQs
What is the greatest common factor?
The greatest common factor is the largest whole number that divides two or more numbers with no remainder. It is also called the greatest common divisor (GCD). For 24 and 36 it is 12.
Source Microsoft Support · GCD function (greatest common divisor), with examples ↗
How do you find the greatest common factor?
Divide the larger number by the smaller, then divide the smaller number by the remainder, and repeat until the remainder is 0. The last number you divided by is the GCF. For small numbers you can also list the factors of each number and pick the biggest one they share.
Source NIST · Dictionary of Algorithms and Data Structures: Euclid's algorithm ↗
What are the greatest common factors of 24 and 36?
The greatest common factor of 24 and 36 is 12. Their common factors are 1, 2, 3, 4, 6 and 12, and 12 is the largest.
Source Microsoft Support · GCD function (greatest common divisor), with examples ↗
Sources
- Microsoft Support: GCD function (greatest common divisor), with examples
- NIST: Dictionary of Algorithms and Data Structures: Euclid's algorithm
- Common Core State Standards: Grade 6, The Number System (6.NS.B.4)