Divisors of 23328: All 42 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 23328

The number 23328 has 42 divisors:

1,  2,  3,  4,  6,  8,  9,  12,  16,  18,  24,  27,  32,  36,  48,  54,  72,  81,  96,  108,  144,  162,  216,  243,  288,  324,  432,  486,  648,  729,  864,  972,  1296,  1458,  1944,  2592,  2916,  3888,  5832,  7776,  11664,  23328

Divisor Pairs of 23328

Each pair multiplies to 23328:

Number of Divisors

The number 23328 has 42 divisors, written as τ(23328) = 42 in number theory.

Sum of Divisors

σ(23328) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 72 + 81 + 96 + 108 + 144 + 162 + 216 + 243 + 288 + 324 + 432 + 486 + 648 + 729 + 864 + 972 + 1296 + 1458 + 1944 + 2592 + 2916 + 3888 + 5832 + 7776 + 11664 + 23328 = 68859

Prime Factorization of 23328

See the full prime factorization calculator →

Properties of 23328

• 23328 is composite.
• 23328 is not a perfect square.
• Number of divisors: 42.
• Sum of divisors: 68859.

Common Divisors with Another Number?

Looking for the divisors that 23328 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 23328

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √23328 ≈ 152.74. If i divides 23328, then both i and 23328/i are divisors.

1. 1 divides 23328 (23328 ÷ 1 = 23328) → pair (1, 23328)
2. 2 divides 23328 (23328 ÷ 2 = 11664) → pair (2, 11664)
3. 3 divides 23328 (23328 ÷ 3 = 7776) → pair (3, 7776)
4. 4 divides 23328 (23328 ÷ 4 = 5832) → pair (4, 5832)
5. 6 divides 23328 (23328 ÷ 6 = 3888) → pair (6, 3888)
6. 8 divides 23328 (23328 ÷ 8 = 2916) → pair (8, 2916)
7. 9 divides 23328 (23328 ÷ 9 = 2592) → pair (9, 2592)
8. 12 divides 23328 (23328 ÷ 12 = 1944) → pair (12, 1944)
9. 16 divides 23328 (23328 ÷ 16 = 1458) → pair (16, 1458)
10. 18 divides 23328 (23328 ÷ 18 = 1296) → pair (18, 1296)
11. 24 divides 23328 (23328 ÷ 24 = 972) → pair (24, 972)
12. 27 divides 23328 (23328 ÷ 27 = 864) → pair (27, 864)
13. 32 divides 23328 (23328 ÷ 32 = 729) → pair (32, 729)
14. 36 divides 23328 (23328 ÷ 36 = 648) → pair (36, 648)
15. 48 divides 23328 (23328 ÷ 48 = 486) → pair (48, 486)
16. 54 divides 23328 (23328 ÷ 54 = 432) → pair (54, 432)
17. 72 divides 23328 (23328 ÷ 72 = 324) → pair (72, 324)
18. 81 divides 23328 (23328 ÷ 81 = 288) → pair (81, 288)
19. 96 divides 23328 (23328 ÷ 96 = 243) → pair (96, 243)
20. 108 divides 23328 (23328 ÷ 108 = 216) → pair (108, 216)
21. 144 divides 23328 (23328 ÷ 144 = 162) → pair (144, 162)
22. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 729, 864, 972, 1296, 1458, 1944, 2592, 2916, 3888, 5832, 7776, 11664, 23328} — total 42 divisors.
23. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 72 + 81 + 96 + 108 + 144 + 162 + 216 + 243 + 288 + 324 + 432 + 486 + 648 + 729 + 864 + 972 + 1296 + 1458 + 1944 + 2592 + 2916 + 3888 + 5832 + 7776 + 11664 + 23328 = 68859.

Nearby Examples

Related Operations for 23328

• Multiples of a Number — "outward" complement of divisors
• 23328 Prime Factorization — decompose into prime building blocks
• Find GCF of 23328 and another number
• Find LCM of 23328 and another number
• Is 23328 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)

Divisors Calculation Examples

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