Divisors of 31968: All 48 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 31968

The number 31968 has 48 divisors:

1,  2,  3,  4,  6,  8,  9,  12,  16,  18,  24,  27,  32,  36,  37,  48,  54,  72,  74,  96,  108,  111,  144,  148,  216,  222,  288,  296,  333,  432,  444,  592,  666,  864,  888,  999,  1184,  1332,  1776,  1998,  2664,  3552,  3996,  5328,  7992,  10656,  15984,  31968

Divisor Pairs of 31968

Each pair multiplies to 31968:

Number of Divisors

The number 31968 has 48 divisors, written as τ(31968) = 48 in number theory.

Sum of Divisors

σ(31968) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 37 + 48 + 54 + 72 + 74 + 96 + 108 + 111 + 144 + 148 + 216 + 222 + 288 + 296 + 333 + 432 + 444 + 592 + 666 + 864 + 888 + 999 + 1184 + 1332 + 1776 + 1998 + 2664 + 3552 + 3996 + 5328 + 7992 + 10656 + 15984 + 31968 = 95760

Prime Factorization of 31968

See the full prime factorization calculator →

Properties of 31968

• 31968 is composite.
• 31968 is not a perfect square.
• Number of divisors: 48.
• Sum of divisors: 95760.

Common Divisors with Another Number?

Looking for the divisors that 31968 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 31968

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √31968 ≈ 178.80. If i divides 31968, then both i and 31968/i are divisors.

1. 1 divides 31968 (31968 ÷ 1 = 31968) → pair (1, 31968)
2. 2 divides 31968 (31968 ÷ 2 = 15984) → pair (2, 15984)
3. 3 divides 31968 (31968 ÷ 3 = 10656) → pair (3, 10656)
4. 4 divides 31968 (31968 ÷ 4 = 7992) → pair (4, 7992)
5. 6 divides 31968 (31968 ÷ 6 = 5328) → pair (6, 5328)
6. 8 divides 31968 (31968 ÷ 8 = 3996) → pair (8, 3996)
7. 9 divides 31968 (31968 ÷ 9 = 3552) → pair (9, 3552)
8. 12 divides 31968 (31968 ÷ 12 = 2664) → pair (12, 2664)
9. 16 divides 31968 (31968 ÷ 16 = 1998) → pair (16, 1998)
10. 18 divides 31968 (31968 ÷ 18 = 1776) → pair (18, 1776)
11. 24 divides 31968 (31968 ÷ 24 = 1332) → pair (24, 1332)
12. 27 divides 31968 (31968 ÷ 27 = 1184) → pair (27, 1184)
13. 32 divides 31968 (31968 ÷ 32 = 999) → pair (32, 999)
14. 36 divides 31968 (31968 ÷ 36 = 888) → pair (36, 888)
15. 37 divides 31968 (31968 ÷ 37 = 864) → pair (37, 864)
16. 48 divides 31968 (31968 ÷ 48 = 666) → pair (48, 666)
17. 54 divides 31968 (31968 ÷ 54 = 592) → pair (54, 592)
18. 72 divides 31968 (31968 ÷ 72 = 444) → pair (72, 444)
19. 74 divides 31968 (31968 ÷ 74 = 432) → pair (74, 432)
20. 96 divides 31968 (31968 ÷ 96 = 333) → pair (96, 333)
21. 108 divides 31968 (31968 ÷ 108 = 296) → pair (108, 296)
22. 111 divides 31968 (31968 ÷ 111 = 288) → pair (111, 288)
23. 144 divides 31968 (31968 ÷ 144 = 222) → pair (144, 222)
24. 148 divides 31968 (31968 ÷ 148 = 216) → pair (148, 216)
25. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 37, 48, 54, 72, 74, 96, 108, 111, 144, 148, 216, 222, 288, 296, 333, 432, 444, 592, 666, 864, 888, 999, 1184, 1332, 1776, 1998, 2664, 3552, 3996, 5328, 7992, 10656, 15984, 31968} — total 48 divisors.
26. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 37 + 48 + 54 + 72 + 74 + 96 + 108 + 111 + 144 + 148 + 216 + 222 + 288 + 296 + 333 + 432 + 444 + 592 + 666 + 864 + 888 + 999 + 1184 + 1332 + 1776 + 1998 + 2664 + 3552 + 3996 + 5328 + 7992 + 10656 + 15984 + 31968 = 95760.

Nearby Examples

Related Operations for 31968

• Multiples of a Number — "outward" complement of divisors
• 31968 Prime Factorization — decompose into prime building blocks
• Find GCF of 31968 and another number
• Find LCM of 31968 and another number
• Is 31968 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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