How to find the factors of 30
Test every whole number from 1 up to the square root of 30 (√30 ≈ 5.477). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 30 ÷ 1 = 30 — so 1 and 30 are factors
- 30 ÷ 2 = 15 — so 2 and 15 are factors
- 30 ÷ 3 = 10 — so 3 and 10 are factors
- 30 ÷ 4 = 7.5 — not a whole number
- 30 ÷ 5 = 6 — so 5 and 6 are factors
Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 5, 6, 10, 15 and 30.
Prime factorization of 30
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 30 = 2 × 3 × 5. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.
Properties of 30
- 30 is a composite number.
- The sum of all its factors is 72; the sum of its proper factors (excluding 30) is 42, which makes it a abundant number (its proper factors add up to more than itself).
- 30 is not a perfect square, so its factors pair up evenly.
- Multiples of 30 include 60, 90, 120, 150 and so on.
Factors vs. multiples
Factors of 30 are the numbers that divide into it; multiples of 30 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 30?
The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. Each of these divides 30 with no remainder.
How many factors does 30 have?
30 has 8 positive factors, which form 4 factor pairs. Counting negative factors as well doubles that to 16.
What is the prime factorization of 30?
30 = 2 × 3 × 5. Its distinct prime factors are 2, 3 and 5.
Is 30 a prime number?
No. 30 is composite because it has 8 factors, more than the two a prime number has.