What are the factor pairs of 24?

The pairs are (1, 24), (2, 12), (3, 8) and (4, 6). Each pair multiplies to 24.

What is the greatest common factor of 24 and 36?

The GCF of 24 and 36 is 12. The common factors are 1, 2, 3, 4, 6 and 12, and 12 is the largest.

Factors of 24 - Factor Pairs & Prime Factorization

Q: What are the factors of 24?

The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. That is eight factors, and each one divides 24 exactly.

Q: What is the prime factorization of 24?

24 = 2 × 2 × 2 × 3 = 2³ × 3. Its prime factors are 2 and 3.

What Are the Factors of 24?

There are 24 hours in a day, and that is no accident. You can split a day into 2 shifts of 12 hours, 3 shifts of 8 hours, 4 shifts of 6 hours and more. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. That is eight factors.

Factor Pairs of 24

Look for pairs that multiply to 24, working from the outside in.

Handwritten notebook page titled Factors of 24 showing 1 × 24, 2 × 12, 3 × 8 and 4 × 6 all equal to 24, with the eight factors 1, 2, 3, 4, 6, 8, 12 and 24 circled in red and the note 8 factors — The four pairs of 24, with every factor circled.

Start with 1 × 24.
Try 2. Since 24 ÷ 2 = 12, write 2 × 12.
Try 3. Since 24 ÷ 3 = 8, write 3 × 8.
Try 4. Since 24 ÷ 4 = 6, write 4 × 6.
Try 5. It leaves a remainder, so skip it. The next number, 6, is already in your list, so you are done.

Prime Factorization of 24

Prime factors show what 24 is built from. Split it and keep going until every branch is a prime.

Handwritten factor tree of 24 splitting into 4 and 6, then 4 into 2 and 2 and 6 into 2 and 3, with the primes circled in red and 24 = 2 × 2 × 2 × 3 = 2³ × 3 written below — Factor tree of 24. The circled primes are 2, 2, 2 and 3.

So 24 = 2 × 2 × 2 × 3 = 2³ × 3. Its prime factors are 2 and 3. Add 1 to each exponent and multiply: (3 + 1) × (1 + 1) = 8, which matches the list.

Divisibility check for 24

A number divides by 24 when it divides by both 8 and 3. Take 168: its last three digits give 168 ÷ 8 = 21, and its digits add up to 15, which is a multiple of 3. So 168 is a multiple of 24.

Is 24 a Prime or Composite Number?

Composite. It has eight factors. The sum of all factors is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60. The factors smaller than 24 add up to 36, which is more than 24 itself, so 24 is called an abundant number.

Real-Life Uses of the Factors of 24

A day. Twenty-four hours split into two 12-hour halves, three 8-hour shifts or four 6-hour blocks.
Eggs and cans. A case of 24 divides into 2 rows of 12, 3 rows of 8 or 4 rows of 6.
Sharing. Twenty-four stickers share evenly between 2, 3, 4, 6, 8 or 12 friends.

Common Factors of 24 With Other Numbers

The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40, so 24 and 40 share 1, 2, 4 and 8. The GCF is 8, which simplifies 24/40 to 3/5.

Quick Practice

Which of these are factors of 24: 5, 6 or 9? Only 6. Now try 48 and check it with the calculator.

Factors of 24