Mathematics · Number Theory
Factor Calculator — All Factors, Factor Pairs & Prime Factorisation
List all the factors (divisors) of a whole number up to 1 trillion, its factor pairs, and its prime factorisation in exponent form. Also tells you whether it's prime, a perfect square or cube, a perfect number, and the count and sum of its divisors.
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Prime Factorisation
2³ × 3² × 5
360 is composite, even
- All 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, 360
- Factor Pairs
- 1 × 360 · 2 × 180 · 3 × 120 · 4 × 90 · 5 × 72 · 6 × 60 · 8 × 45 · 9 × 40 · 10 × 36 · 12 × 30 · 15 × 24 · 18 × 20
- Sum of Factors
- 1,170 (proper factors: 810)
- Prime Factors
- 2, 3, 5
How this is calculated
n = p₁^a × p₂^b × … · number of factors = (a + 1)(b + 1)… · sum of factors = Π (p^(a+1) − 1) ÷ (p − 1)
- p
- Prime factors of n
Divide by the smallest prime that goes in exactly, again and again, until only 1 is left: 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5. Every factor of 360 is a product of some of those primes, which is why it has (3 + 1)(2 + 1)(1 + 1) = 24 factors.
Assumptions & sources
- Positive whole numbers up to 10¹².
Calculator ID MATH-FACTORS-001 · version 1.0.0
Common questions
What are the factors of 360?
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, 360.
Is 1 a prime number?
No — a prime has exactly two factors, 1 and itself. 1 has only one.
What is a perfect number?
One equal to the sum of its other factors, like 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14.