Divisors of 960: All 28 Factors

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 960

The number 960 has 28 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  16,  20,  24,  30,  32,  40,  48,  60,  64,  80,  96,  120,  160,  192,  240,  320,  480,  960

Divisor Pairs of 960

Each pair multiplies to 960:

Number of Divisors

The number 960 has 28 divisors, written as τ(960) = 28 in number theory.

Sum of Divisors

σ(960) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 64 + 80 + 96 + 120 + 160 + 192 + 240 + 320 + 480 + 960 = 3048

Prime Factorization of 960

See the full prime factorization calculator →

Properties of 960

• 960 is composite.
• 960 is not a perfect square.
• Number of divisors: 28.
• Sum of divisors: 3048.

Common Divisors with Another Number?

Looking for the divisors that 960 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 960

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √960 ≈ 30.98. If i divides 960, then both i and 960/i are divisors.

1. 1 divides 960 (960 ÷ 1 = 960) → pair (1, 960)
2. 2 divides 960 (960 ÷ 2 = 480) → pair (2, 480)
3. 3 divides 960 (960 ÷ 3 = 320) → pair (3, 320)
4. 4 divides 960 (960 ÷ 4 = 240) → pair (4, 240)
5. 5 divides 960 (960 ÷ 5 = 192) → pair (5, 192)
6. 6 divides 960 (960 ÷ 6 = 160) → pair (6, 160)
7. 8 divides 960 (960 ÷ 8 = 120) → pair (8, 120)
8. 10 divides 960 (960 ÷ 10 = 96) → pair (10, 96)
9. 12 divides 960 (960 ÷ 12 = 80) → pair (12, 80)
10. 15 divides 960 (960 ÷ 15 = 64) → pair (15, 64)
11. 16 divides 960 (960 ÷ 16 = 60) → pair (16, 60)
12. 20 divides 960 (960 ÷ 20 = 48) → pair (20, 48)
13. 24 divides 960 (960 ÷ 24 = 40) → pair (24, 40)
14. 30 divides 960 (960 ÷ 30 = 32) → pair (30, 32)
15. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960} — total 28 divisors.
16. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 64 + 80 + 96 + 120 + 160 + 192 + 240 + 320 + 480 + 960 = 3048.

Nearby Examples

Related Operations for 960

• Multiples of 960 — "outward" complement; M is a multiple of 960 ⇔ 960 is a divisor of M
• 960 Prime Factorization — decompose into prime building blocks
• Find GCF of 960 and another number
• Find LCM of 960 and another number
• Is 960 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

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.

References

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

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