What are the prime factors of 12?

The prime factors of 12 are 2 and 3. Written as a full prime factorization, 12 = 2 × 2 × 3 = 2² × 3.

What are the factor pairs of 12?

The positive factor pairs of 12 are (1, 12), (2, 6) and (3, 4). Each pair multiplies to 12.

Factors of 12 - Factor Pairs & Prime Factorization

Q: What are the factors of 12?

The factors of 12 are 1, 2, 3, 4, 6 and 12. Each one divides 12 with no remainder, so 12 has six factors in total.

Q: Is 12 a prime or composite number?

Composite. A prime has exactly two factors, but 12 has six, so it can be split into smaller whole-number pieces.

What Are the Factors of 12?

Picture a carton of 12 eggs. You can line them up as 1 long row of 12, 2 rows of 6, 3 rows of 4, 4 rows of 3, 6 rows of 2, or 12 rows of 1. Every one of those neat layouts is a factor hiding in plain sight.

A factor is a whole number that divides another number exactly, with nothing left over. The factors of 12 are 1, 2, 3, 4, 6 and 12. That is six numbers, and 12 is the smallest number in the world that has exactly six factors.

Factor Pairs of 12: Meet in the Middle

Here is the trick I show every student. Do not hunt for factors one at a time. Hunt for pairs that multiply to 12, and work from the outside in.

Handwritten notebook page titled Factors of 12 showing 1 × 12, 2 × 6 and 3 × 4, with the six factors 1, 2, 3, 4, 6 and 12 circled in red and the note 6 factors — The three pairs of 12, then every factor circled in order.

Start with 1 × 12. Every number has this pair.
Try 2. Since 12 ÷ 2 = 6, write 2 × 6.
Try 3. Since 12 ÷ 3 = 4, write 3 × 4.
Try 4. It is already in your list, so you have met in the middle and you are done.

When the next number you test is already written down, stop. There are no more pairs to find.

Prime Factorization of 12 With a Factor Tree

Factors tell you everything that divides 12. Prime factors tell you what 12 is built from. Split 12 into any two numbers that multiply to it, then keep splitting until every branch is a prime.

Handwritten factor tree of 12 splitting into 3 and 4, then 4 into 2 and 2, with the primes 3, 2 and 2 circled in red and 12 = 2 × 2 × 3 = 2² × 3 written below — Factor tree of 12. The circled primes are where each branch stops.

So 12 = 2 × 2 × 3 = 2² × 3. If you had started with 2 × 6 instead, you would land on the very same primes. That is no accident: every number has exactly one prime factorization.

Count the factors without listing them

Add 1 to each exponent and multiply. For 2² × 3¹ that gives (2 + 1) × (1 + 1) = 6, which matches our list. This shortcut becomes a lifesaver for bigger numbers.

Is 12 a Prime or Composite Number?

Composite. A prime has only two factors, 1 and itself, while 12 has six. It is also a bit special: add up its factors except 12 itself and you get 1 + 2 + 3 + 4 + 6 = 16, which is bigger than 12. Mathematicians call that an abundant number, and 12 is the smallest one. The sum of all six factors is 28.

Why 12 Is Everywhere: Real-Life Uses of Its Factors

A dozen eggs or donuts can be shared fairly between 1, 2, 3, 4, 6 or 12 people.
A clock face has 12 hours, so quarters (3 hours), thirds (4 hours) and halves (6 hours) all land on whole numbers.
A foot is 12 inches, which is why half a foot is 6 inches and a third of a foot is exactly 4.

Common Factors of 12 With Other Numbers

The greatest common factor (GCF) is the biggest factor two numbers share. The factors of 18 are 1, 2, 3, 6, 9 and 18, so the common factors of 12 and 18 are 1, 2, 3 and 6, and the GCF is 6. With 20 the GCF is 4. You use the GCF to simplify fractions: 8/12 becomes 2/3 after dividing the top and bottom by 4.

Quick Practice

Which of these are factors of 12: 5, 6 or 8? Only 6. 12 ÷ 5 leaves 2 and 12 ÷ 8 leaves 4. Now try 24 yourself and check your list with the calculator.

Factors of 12