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Factors of 360

360 has 24 factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360. Its prime factorization is 2³ × 3² × 5.

Factor pairs of 360

Factor×FactorProduct
1×360360
2×180360
3×120360
4×90360
5×72360
6×60360
8×45360
9×40360
10×36360
12×30360
15×24360
18×20360

Negative pairs work too: (−1) × (−360), (−2) × (−180), … = 360.

Number of factors
24
Factor pairs
12
Sum of factors
1,170
Prime or composite
Composite
Even or odd
Even
Perfect square
No
Prime factorization 2³ × 3² × 5

How to find the factors of 360

Test every whole number from 1 up to the square root of 360 (√360 ≈ 18.974). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

  • 360 ÷ 1 = 360 — so 1 and 360 are factors
  • 360 ÷ 2 = 180 — so 2 and 180 are factors
  • 360 ÷ 3 = 120 — so 3 and 120 are factors
  • 360 ÷ 4 = 90 — so 4 and 90 are factors
  • 360 ÷ 5 = 72 — so 5 and 72 are factors
  • 360 ÷ 6 = 60 — so 6 and 60 are factors
  • 360 ÷ 7 = 51.429 — not a whole number
  • 360 ÷ 8 = 45 — so 8 and 45 are factors
  • 360 ÷ 9 = 40 — so 9 and 40 are factors
  • 360 ÷ 10 = 36 — so 10 and 36 are factors
  • 360 ÷ 11 = 32.727 — not a whole number
  • 360 ÷ 12 = 30 — so 12 and 30 are factors
  • 360 ÷ 13 = 27.692 — not a whole number
  • 360 ÷ 14 = 25.714 — not a whole number
  • 360 ÷ 15 = 24 — so 15 and 24 are factors
  • 360 ÷ 16 = 22.5 — not a whole number
  • 360 ÷ 17 = 21.176 — not a whole number
  • 360 ÷ 18 = 20 — so 18 and 20 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360.

Prime factorization of 360

Divide by the smallest prime that fits, and keep going until the quotient is 1:

360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

The primes you divided by give 360 = 2³ × 3² × 5. From the exponents you can also count the factors without listing them: (3 + 1) × (2 + 1) × (1 + 1) = 24.

Properties of 360

  • 360 is a composite number.
  • The sum of all its factors is 1,170; the sum of its proper factors (excluding 360) is 810, which makes it a abundant number (its proper factors add up to more than itself).
  • 360 is not a perfect square, so its factors pair up evenly.
  • Multiples of 360 include 720, 1,080, 1,440, 1,800 and so on.

Factors vs. multiples

Factors of 360 are the numbers that divide into it; multiples of 360 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 360?

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360. Each of these divides 360 with no remainder.

How many factors does 360 have?

360 has 24 positive factors, which form 12 factor pairs. Counting negative factors as well doubles that to 48.

What is the prime factorization of 360?

360 = 2³ × 3² × 5. Its distinct prime factors are 2, 3 and 5.

Is 360 a prime number?

No. 360 is composite because it has 24 factors, more than the two a prime number has.