What are the factor pairs of 54?

The pairs are (1, 54), (2, 27), (3, 18) and (6, 9). Each pair multiplies to 54.

What is the greatest common factor of 54 and 72?

The GCF of 54 and 72 is 18. The common factors are 1, 2, 3, 6, 9 and 18, and 18 is the largest.

Factors of 54 - Factor Pairs & Prime Factorization

Q: What are the factors of 54?

The factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54. That is eight factors, and each one divides 54 exactly.

Q: What is the prime factorization of 54?

54 = 2 × 3 × 3 × 3 = 2 × 3³. Its prime factors are 2 and 3.

What Are the Factors of 54?

A deck of cards with both jokers has 54 cards, which deal evenly to 2, 3, 6 or 9 players. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.

The factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54. That is eight factors.

Factor Pairs of 54

Look for pairs that multiply to 54, working from the outside in.

Handwritten notebook page titled Factors of 54 showing 1 × 54, 2 × 27, 3 × 18, 6 × 9 all equal to 54, with the eight factors 1, 2, 3, 6, 9, 18, 27 and 54 circled in red and the note 8 factors — The 4 pairs of 54, with every factor circled.

Start with 1 × 54.
Try 2. Since 54 ÷ 2 = 27, write 2 × 27.
Try 3. Since 54 ÷ 3 = 18, write 3 × 18.
Try 6. Since 54 ÷ 6 = 9, write 6 × 9.
Keep trying whole numbers until you reach 9, which is already in your list. Every factor is now found, so you are done.

Prime Factorization of 54

Prime factors show what 54 is built from. Split it and keep going until every branch is a prime.

Handwritten factor tree of 54 splitting down to the circled primes 2, 3, 3 and 3, with 54 = 2 × 3 × 3 × 3 = 2 × 3³ written below — Factor tree of 54. The circled primes are 2, 3, 3 and 3.

So 54 = 2 × 3 × 3 × 3 = 2 × 3³. Its prime factors are 2 and 3. Add 1 to each exponent and multiply: (1 + 1) × (3 + 1) = 8, which matches the list.

Divisibility check for 54

A number divides by 54 when it divides by 2 and 27. Take 162: it is even and 162 ÷ 27 = 6, so 162 is a multiple of 54.

Is 54 a Prime or Composite Number?

Composite. It has eight factors. The sum of all factors is 1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 = 120. The factors smaller than 54 add up to 66, which is more than 54, so 54 is called an abundant number.

Real-Life Uses of the Factors of 54

Playing cards. A deck with both jokers has 54 cards, and it deals evenly to 2, 3, 6 or 9 players.
Tiles. Fifty-four tiles fit in 6 rows of 9 or 3 rows of 18.
Sharing. Fifty-four stickers share evenly between 2, 3, 6, 9, 18 or 27 people.

Common Factors of 54 With Other Numbers

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72, so 54 and 72 share 1, 2, 3, 6, 9 and 18. The GCF is 18, which simplifies 54/72 to 3/4.

Quick Practice

Which of these are factors of 54: 5, 6 or 8? Only 6. Now try 56 and check it with the calculator.

Factors of 54