Divisors of 972: All 18 Factors
Quick Answer
972 has 18 divisors (factors): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.
Sum: 2548.
Divisors (Factors) Calculator
Use the calculator above to find all divisors (also called factors) of any positive integer up to 4,782,969. Beyond the divisor list, this tool also shows divisor pairs, the sum and count of divisors, prime factorization, and number properties (prime, perfect square, perfect number).
All Divisors of 972
The number 972 has 18 divisors:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
Divisor Pairs of 972
Each pair multiplies to 972:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 972 | = | 972 |
| 2 | × | 486 | = | 972 |
| 3 | × | 324 | = | 972 |
| 4 | × | 243 | = | 972 |
| 6 | × | 162 | = | 972 |
| 9 | × | 108 | = | 972 |
| 12 | × | 81 | = | 972 |
| 18 | × | 54 | = | 972 |
| 27 | × | 36 | = | 972 |
Number of Divisors
The number 972 has 18 divisors, written as τ(972) = 18 in number theory.
Sum of Divisors
σ(972) = 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 243 + 324 + 486 + 972 = 2548
Prime Factorization of 972
Properties of 972
- 972 is composite.
- 972 is not a perfect square.
- Number of divisors: 18.
- Sum of divisors: 2548.
Common Divisors with Another Number?
Looking for the divisors that 972 shares with another number? Use our Greatest Common Factor (GCF) calculator — it finds all common divisors and the largest one.
Step-by-Step: How to Find the Divisors of 972
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √972 ≈ 31.18. If i divides 972, then both i and 972/i are divisors.
- 1 divides 972 (972 ÷ 1 = 972) → pair (1, 972)
- 2 divides 972 (972 ÷ 2 = 486) → pair (2, 486)
- 3 divides 972 (972 ÷ 3 = 324) → pair (3, 324)
- 4 divides 972 (972 ÷ 4 = 243) → pair (4, 243)
- 6 divides 972 (972 ÷ 6 = 162) → pair (6, 162)
- 9 divides 972 (972 ÷ 9 = 108) → pair (9, 108)
- 12 divides 972 (972 ÷ 12 = 81) → pair (12, 81)
- 18 divides 972 (972 ÷ 18 = 54) → pair (18, 54)
- 27 divides 972 (972 ÷ 27 = 36) → pair (27, 36)
- Collect all unique values: {1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972} — total 18 divisors.
- Sum: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 243 + 324 + 486 + 972 = 2548.
Nearby Examples
Related Operations for 972
- Multiples of 972 — "outward" complement; M is a multiple of 972 ⇔ 972 is a divisor of M
- 972 Prime Factorization — decompose into prime building blocks
- Find GCF of 972 and another number
- Find LCM of 972 and another number
- Is 972 a perfect square? (odd divisor count ⇔ yes)
See also our tables of divisors:
What Is a Divisor?
A divisor (also called a factor) of a positive integer n is any positive integer d such that n ÷ d has no remainder. In other words, d divides n evenly.
Every positive integer n has at least two divisors: 1 and n itself (with 1 being the trivial case of having only itself). Numbers with exactly 2 divisors are prime; numbers with 3 or more divisors are composite.
Why use this calculator? Beyond just listing divisors, this tool computes the sum σ(n), the count τ(n), prime factorization, divisor pairs (useful for visual learners and factoring problems), and detects whether n is a prime, a perfect square, or a perfect number.
Divisors Calculation Examples
Find all divisors of these numbers:
Related Calculators
- Multiples of a Number — "outward" complement
- Prime Factorization — product of prime divisors
- Greatest Common Factor (GCF) — largest common divisor of 2+ numbers
- Least Common Multiple (LCM) — smallest common multiple
- Is N a Perfect Square? — odd divisor count check