How to find the factors of 45
Test every whole number from 1 up to the square root of 45 (√45 ≈ 6.708). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 45 ÷ 1 = 45 — so 1 and 45 are factors
- 45 ÷ 2 = 22.5 — not a whole number
- 45 ÷ 3 = 15 — so 3 and 15 are factors
- 45 ÷ 4 = 11.25 — not a whole number
- 45 ÷ 5 = 9 — so 5 and 9 are factors
- 45 ÷ 6 = 7.5 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1, 3, 5, 9, 15 and 45.
Prime factorization of 45
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 45 = 3² × 5. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) = 6.
Properties of 45
- 45 is a composite number.
- The sum of all its factors is 78; the sum of its proper factors (excluding 45) is 33, which makes it a deficient number (its proper factors add up to less than itself).
- 45 is not a perfect square, so its factors pair up evenly.
- Multiples of 45 include 90, 135, 180, 225 and so on.
Factors vs. multiples
Factors of 45 are the numbers that divide into it; multiples of 45 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 45?
The factors of 45 are 1, 3, 5, 9, 15 and 45. Each of these divides 45 with no remainder.
How many factors does 45 have?
45 has 6 positive factors, which form 3 factor pairs. Counting negative factors as well doubles that to 12.
What is the prime factorization of 45?
45 = 3² × 5. Its distinct prime factors are 3 and 5.
Is 45 a prime number?
No. 45 is composite because it has 6 factors, more than the two a prime number has.