How to find the factors of 54
Test every whole number from 1 up to the square root of 54 (√54 ≈ 7.348). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 54 ÷ 1 = 54 — so 1 and 54 are factors
- 54 ÷ 2 = 27 — so 2 and 27 are factors
- 54 ÷ 3 = 18 — so 3 and 18 are factors
- 54 ÷ 4 = 13.5 — not a whole number
- 54 ÷ 5 = 10.8 — not a whole number
- 54 ÷ 6 = 9 — so 6 and 9 are factors
- 54 ÷ 7 = 7.714 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 6, 9, 18, 27 and 54.
Prime factorization of 54
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 54 = 2 × 3³. From the exponents you can also count the factors without listing them: (1 + 1) × (3 + 1) = 8.
Properties of 54
- 54 is a composite number.
- The sum of all its factors is 120; the sum of its proper factors (excluding 54) is 66, which makes it a abundant number (its proper factors add up to more than itself).
- 54 is not a perfect square, so its factors pair up evenly.
- Multiples of 54 include 108, 162, 216, 270 and so on.
Factors vs. multiples
Factors of 54 are the numbers that divide into it; multiples of 54 are the numbers it divides into. Every number has a limited set of factors but infinitely many multiples. To work with any other number, use the factors calculator, or find shared factors with the GCF calculator.
Frequently asked questions
What are the factors of 54?
The factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54. Each of these divides 54 with no remainder.
How many factors does 54 have?
54 has 8 positive factors, which form 4 factor pairs. Counting negative factors as well doubles that to 16.
What is the prime factorization of 54?
54 = 2 × 3³. Its distinct prime factors are 2 and 3.
Is 54 a prime number?
No. 54 is composite because it has 8 factors, more than the two a prime number has.