Quick lookup, 1-20
GCF Reference Chart
This chart shows the greatest common factor (GCF) for every pair of whole numbers from 1 to 20 at a glance, useful for checking a homework answer quickly or spotting a pattern without running the calculator each time. Find your first number down the left column and your second number along the top row; the cell where they meet is the GCF of that pair. For numbers outside this 1-20 range, or for three or more numbers at once, use the calculator on the homepage, which handles any whole numbers and shows the full prime factorization work as well.
| GCF | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 |
| 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 |
| 4 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 4 |
| 5 | 1 | 1 | 1 | 1 | 5 | 1 | 1 | 1 | 1 | 5 | 1 | 1 | 1 | 1 | 5 | 1 | 1 | 1 | 1 | 5 |
| 6 | 1 | 2 | 3 | 2 | 1 | 6 | 1 | 2 | 3 | 2 | 1 | 6 | 1 | 2 | 3 | 2 | 1 | 6 | 1 | 2 |
| 7 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | 1 | 1 | 1 | 1 | 1 | 1 |
| 8 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 8 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 8 | 1 | 2 | 1 | 4 |
| 9 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 9 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 9 | 1 | 1 |
| 10 | 1 | 2 | 1 | 2 | 5 | 2 | 1 | 2 | 1 | 10 | 1 | 2 | 1 | 2 | 5 | 2 | 1 | 2 | 1 | 10 |
| 11 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 11 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 12 | 1 | 2 | 3 | 4 | 1 | 6 | 1 | 4 | 3 | 2 | 1 | 12 | 1 | 2 | 3 | 4 | 1 | 6 | 1 | 4 |
| 13 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 13 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 14 | 1 | 2 | 1 | 2 | 1 | 2 | 7 | 2 | 1 | 2 | 1 | 2 | 1 | 14 | 1 | 2 | 1 | 2 | 1 | 2 |
| 15 | 1 | 1 | 3 | 1 | 5 | 3 | 1 | 1 | 3 | 5 | 1 | 3 | 1 | 1 | 15 | 1 | 1 | 3 | 1 | 5 |
| 16 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 8 | 1 | 2 | 1 | 4 | 1 | 2 | 1 | 16 | 1 | 2 | 1 | 4 |
| 17 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 17 | 1 | 1 | 1 |
| 18 | 1 | 2 | 3 | 2 | 1 | 6 | 1 | 2 | 9 | 2 | 1 | 6 | 1 | 2 | 3 | 2 | 1 | 18 | 1 | 2 |
| 19 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 19 | 1 |
| 20 | 1 | 2 | 1 | 4 | 5 | 2 | 1 | 4 | 1 | 10 | 1 | 4 | 1 | 2 | 5 | 4 | 1 | 2 | 1 | 20 |
Highlighted cells: a shaded diagonal marks where a number's GCF with itself equals that number (or a clean multiple), and a lighter tint marks coprime pairs (GCF = 1, no common factor besides 1).
How to read the chart
The chart is symmetric, meaning GCF(6, 15) and GCF(15, 6) give the same answer, so it doesn't matter which number you look up first, down the side or across the top. The shaded diagonal cells (where a number's GCF with itself equals that number) confirm the basic rule that any number's GCF with itself is always itself. The lighter, coprime cells (where the GCF is 1) mark pairs that share no common factor larger than 1, which happens more often than many people expect, roughly 6 out of every 10 randomly chosen pairs of whole numbers are coprime. For numbers outside this 1-20 range, or three or more numbers at once, use the GCF calculator, or see how to find the GCF for the methods behind this table.
A few commonly looked-up values, called out directly
Some specific pairs come up in schoolwork more than others, usually because they appear in a common fraction-simplifying or word-problem example. Here are a handful, matching the chart above:
- GCF of 12 and 18 is 6
- GCF of 15 and 20 is 5
- GCF of 16 and 24 is 8
- GCF of 9 and 12 is 3
- GCF of 10 and 15 is 5
- GCF of 8 and 12 is 4
- GCF of 14 and 21 is 7
- GCF of 18 and 24 is 6
What this chart doesn't cover, and why
This table is capped at 20 by 20 on purpose: a larger printed grid becomes hard to scan visually and the pattern it's meant to illustrate (how common factors relate to multiples) is already clear by 20. If you need the GCF of a number larger than 20, or the GCF of three or more numbers at once, those cases go beyond what a two-dimensional table can show cleanly, that's exactly what the calculator on the homepage is for: it accepts any whole numbers up to fifteen at a time and shows the same kind of step-by-step prime factorization work this chart is built from, just computed on demand instead of pre-listed.
The pattern behind the diagonal and near-diagonal cells
Look along the top-left to bottom-right diagonal of the chart and you'll see every number matched with itself, always equal to that number, since any number divides itself with no remainder. One step off that diagonal (comparing a number to its immediate neighbors) tends to produce a GCF of 1 far more often than not, because two consecutive whole numbers can never share any common factor larger than 1; if they did, that factor would also have to divide their difference, which is always exactly 1, and nothing but 1 divides 1. That's why, for example, GCF(7, 8), GCF(12, 13) and GCF(19, 20) are all 1, a rule that holds for every pair of consecutive whole numbers, not just the ones shown on this particular 20-by-20 grid.
Frequently asked questions
Why is the GCF of two consecutive numbers always 1?
Does the chart include 1 as a number?
How do I find the GCF for numbers bigger than 20?
What does it mean if a chart cell shows the same number as the row or column header?
Is this chart generated from data sent to a server?
Need a number outside this chart?
The calculator handles any whole numbers, including three or more at once.
Open the GCF calculatorFree. No sign-up.