Divisors of 20736: All 45 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 20736

The number 20736 has 45 divisors:

1,  2,  3,  4,  6,  8,  9,  12,  16,  18,  24,  27,  32,  36,  48,  54,  64,  72,  81,  96,  108,  128,  144,  162,  192,  216,  256,  288,  324,  384,  432,  576,  648,  768,  864,  1152,  1296,  1728,  2304,  2592,  3456,  5184,  6912,  10368,  20736

Divisor Pairs of 20736

Each pair multiplies to 20736:

Note: the last pair has identical factors (144 × 144) because 20736 is a perfect square.

Number of Divisors

The number 20736 has 45 divisors, written as τ(20736) = 45 in number theory.

⚡ Notice: 20736 has an odd number of divisors — this means 20736 is a perfect square (√20736 = 144).

Sum of Divisors

σ(20736) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 81 + 96 + 108 + 128 + 144 + 162 + 192 + 216 + 256 + 288 + 324 + 384 + 432 + 576 + 648 + 768 + 864 + 1152 + 1296 + 1728 + 2304 + 2592 + 3456 + 5184 + 6912 + 10368 + 20736 = 61831

Prime Factorization of 20736

See the full prime factorization calculator →

Properties of 20736

• 20736 is composite.
• 20736 is a perfect square (√20736 = 144).
• Number of divisors: 45.
• Sum of divisors: 61831.

Common Divisors with Another Number?

Looking for the divisors that 20736 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 20736

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √20736 ≈ 144.00. If i divides 20736, then both i and 20736/i are divisors.

1. 1 divides 20736 (20736 ÷ 1 = 20736) → pair (1, 20736)
2. 2 divides 20736 (20736 ÷ 2 = 10368) → pair (2, 10368)
3. 3 divides 20736 (20736 ÷ 3 = 6912) → pair (3, 6912)
4. 4 divides 20736 (20736 ÷ 4 = 5184) → pair (4, 5184)
5. 6 divides 20736 (20736 ÷ 6 = 3456) → pair (6, 3456)
6. 8 divides 20736 (20736 ÷ 8 = 2592) → pair (8, 2592)
7. 9 divides 20736 (20736 ÷ 9 = 2304) → pair (9, 2304)
8. 12 divides 20736 (20736 ÷ 12 = 1728) → pair (12, 1728)
9. 16 divides 20736 (20736 ÷ 16 = 1296) → pair (16, 1296)
10. 18 divides 20736 (20736 ÷ 18 = 1152) → pair (18, 1152)
11. 24 divides 20736 (20736 ÷ 24 = 864) → pair (24, 864)
12. 27 divides 20736 (20736 ÷ 27 = 768) → pair (27, 768)
13. 32 divides 20736 (20736 ÷ 32 = 648) → pair (32, 648)
14. 36 divides 20736 (20736 ÷ 36 = 576) → pair (36, 576)
15. 48 divides 20736 (20736 ÷ 48 = 432) → pair (48, 432)
16. 54 divides 20736 (20736 ÷ 54 = 384) → pair (54, 384)
17. 64 divides 20736 (20736 ÷ 64 = 324) → pair (64, 324)
18. 72 divides 20736 (20736 ÷ 72 = 288) → pair (72, 288)
19. 81 divides 20736 (20736 ÷ 81 = 256) → pair (81, 256)
20. 96 divides 20736 (20736 ÷ 96 = 216) → pair (96, 216)
21. 108 divides 20736 (20736 ÷ 108 = 192) → pair (108, 192)
22. 128 divides 20736 (20736 ÷ 128 = 162) → pair (128, 162)
23. 144 divides 20736 (20736 ÷ 144 = 144) → pair (144, 144)
24. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 256, 288, 324, 384, 432, 576, 648, 768, 864, 1152, 1296, 1728, 2304, 2592, 3456, 5184, 6912, 10368, 20736} — total 45 divisors.
25. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 64 + 72 + 81 + 96 + 108 + 128 + 144 + 162 + 192 + 216 + 256 + 288 + 324 + 384 + 432 + 576 + 648 + 768 + 864 + 1152 + 1296 + 1728 + 2304 + 2592 + 3456 + 5184 + 6912 + 10368 + 20736 = 61831.

Nearby Examples

Related Operations for 20736

• Multiples of a Number — "outward" complement of divisors
• 20736 Prime Factorization — decompose into prime building blocks
• Find GCF of 20736 and another number
• Find LCM of 20736 and another number
• Is 20736 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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