What are the factor pairs of 48?

The pairs are (1, 48), (2, 24), (3, 16), (4, 12) and (6, 8). Each pair multiplies to 48.

What is the greatest common factor of 48 and 60?

The GCF of 48 and 60 is 12. The common factors are 1, 2, 3, 4, 6 and 12, and 12 is the largest.

Factors of 48 - Factor Pairs & Prime Factorization

Q: What are the factors of 48?

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. That is ten factors, and each one divides 48 exactly.

Q: What is the prime factorization of 48?

48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3. Its prime factors are 2 and 3.

What Are the Factors of 48?

Four dozen eggs makes 48. You can pack them 1 row of 48, 2 rows of 24, 3 rows of 16, 4 rows of 12 or 6 rows of 8, and every tidy layout is a factor. A factor is a whole number that divides another number exactly, with no remainder.

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. That is ten factors.

Factor Pairs of 48

Look for pairs that multiply to 48, working from the outside in.

Handwritten notebook page titled Factors of 48 showing 1 × 48, 2 × 24, 3 × 16, 4 × 12 and 6 × 8 all equal to 48, with the ten factors 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 circled in red and the note 10 factors — The five pairs of 48, with every factor circled.

Start with 1 × 48.
Try 2. Since 48 ÷ 2 = 24, write 2 × 24.
Try 3. Since 48 ÷ 3 = 16, write 3 × 16.
Try 4. Since 48 ÷ 4 = 12, write 4 × 12.
Try 5. It leaves a remainder, so skip it.
Try 6. Since 48 ÷ 6 = 8, write 6 × 8. The next number, 7, does not divide 48 and 8 is already used, so you are done.

Prime Factorization of 48

Prime factors show what 48 is built from. Split it and keep going until every branch is prime.

Handwritten factor tree of 48 splitting into 6 and 8, then 6 into 2 and 3, and 8 into 2 and 4, and 4 into 2 and 2, with the primes circled in red and 48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3 written below — Factor tree of 48. The circled primes are 2, 3, 2, 2 and 2.

So 48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3. Its prime factors are 2 and 3. Add 1 to each exponent and multiply: (4 + 1) × (1 + 1) = 10, which matches the list.

Divisibility check for 48

A number divides by 48 when it divides by both 16 and 3. Take 144: its last digits give 144 ÷ 16 = 9, and its digits add up to 9, a multiple of 3. So 144 is a multiple of 48.

Is 48 a Prime or Composite Number?

Composite. It has ten factors. The sum of all factors is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 124. Since 48 is not a perfect square, every factor has a different partner and the count stays even.

Real-Life Uses of the Factors of 48

Two days. Forty-eight hours is 2 days, and it splits into 4 blocks of 12 hours or 6 blocks of 8 hours.
Four dozen. A 48-pack divides into 4 rows of 12 or 6 rows of 8.
Sharing. Forty-eight candies share evenly between 2, 3, 4, 6, 8, 12, 16 or 24 people.

Common Factors of 48 With Other Numbers

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60, so 48 and 60 share 1, 2, 3, 4, 6 and 12. The GCF is 12, which simplifies 48/60 to 4/5.

Quick Practice

Which of these are factors of 48: 9, 12 or 16? That is 12 and 16. Now try 96 and check it with the calculator.

Factors of 48