Divisors of 59976: All 72 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 59976

The number 59976 has 72 divisors:

1,  2,  3,  4,  6,  7,  8,  9,  12,  14,  17,  18,  21,  24,  28,  34,  36,  42,  49,  51,  56,  63,  68,  72,  84,  98,  102,  119,  126,  136,  147,  153,  168,  196,  204,  238,  252,  294,  306,  357,  392,  408,  441,  476,  504,  588,  612,  714,  833,  882,  952,  1071,  1176,  1224,  1428,  1666,  1764,  2142,  2499,  2856,  3332,  3528,  4284,  4998,  6664,  7497,  8568,  9996,  14994,  19992,  29988,  59976

Divisor Pairs of 59976

Each pair multiplies to 59976:

Number of Divisors

The number 59976 has 72 divisors, written as τ(59976) = 72 in number theory.

Sum of Divisors

σ(59976) = 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 17 + 18 + 21 + 24 + 28 + 34 + 36 + 42 + 49 + 51 + 56 + 63 + 68 + 72 + 84 + 98 + 102 + 119 + 126 + 136 + 147 + 153 + 168 + 196 + 204 + 238 + 252 + 294 + 306 + 357 + 392 + 408 + 441 + 476 + 504 + 588 + 612 + 714 + 833 + 882 + 952 + 1071 + 1176 + 1224 + 1428 + 1666 + 1764 + 2142 + 2499 + 2856 + 3332 + 3528 + 4284 + 4998 + 6664 + 7497 + 8568 + 9996 + 14994 + 19992 + 29988 + 59976 = 200070

Prime Factorization of 59976

See the full prime factorization calculator →

Properties of 59976

• 59976 is composite.
• 59976 is not a perfect square.
• Number of divisors: 72.
• Sum of divisors: 200070.

Common Divisors with Another Number?

Looking for the divisors that 59976 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 59976

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √59976 ≈ 244.90. If i divides 59976, then both i and 59976/i are divisors.

1. 1 divides 59976 (59976 ÷ 1 = 59976) → pair (1, 59976)
2. 2 divides 59976 (59976 ÷ 2 = 29988) → pair (2, 29988)
3. 3 divides 59976 (59976 ÷ 3 = 19992) → pair (3, 19992)
4. 4 divides 59976 (59976 ÷ 4 = 14994) → pair (4, 14994)
5. 6 divides 59976 (59976 ÷ 6 = 9996) → pair (6, 9996)
6. 7 divides 59976 (59976 ÷ 7 = 8568) → pair (7, 8568)
7. 8 divides 59976 (59976 ÷ 8 = 7497) → pair (8, 7497)
8. 9 divides 59976 (59976 ÷ 9 = 6664) → pair (9, 6664)
9. 12 divides 59976 (59976 ÷ 12 = 4998) → pair (12, 4998)
10. 14 divides 59976 (59976 ÷ 14 = 4284) → pair (14, 4284)
11. 17 divides 59976 (59976 ÷ 17 = 3528) → pair (17, 3528)
12. 18 divides 59976 (59976 ÷ 18 = 3332) → pair (18, 3332)
13. 21 divides 59976 (59976 ÷ 21 = 2856) → pair (21, 2856)
14. 24 divides 59976 (59976 ÷ 24 = 2499) → pair (24, 2499)
15. 28 divides 59976 (59976 ÷ 28 = 2142) → pair (28, 2142)
16. 34 divides 59976 (59976 ÷ 34 = 1764) → pair (34, 1764)
17. 36 divides 59976 (59976 ÷ 36 = 1666) → pair (36, 1666)
18. 42 divides 59976 (59976 ÷ 42 = 1428) → pair (42, 1428)
19. 49 divides 59976 (59976 ÷ 49 = 1224) → pair (49, 1224)
20. 51 divides 59976 (59976 ÷ 51 = 1176) → pair (51, 1176)
21. 56 divides 59976 (59976 ÷ 56 = 1071) → pair (56, 1071)
22. 63 divides 59976 (59976 ÷ 63 = 952) → pair (63, 952)
23. 68 divides 59976 (59976 ÷ 68 = 882) → pair (68, 882)
24. 72 divides 59976 (59976 ÷ 72 = 833) → pair (72, 833)
25. 84 divides 59976 (59976 ÷ 84 = 714) → pair (84, 714)
26. 98 divides 59976 (59976 ÷ 98 = 612) → pair (98, 612)
27. 102 divides 59976 (59976 ÷ 102 = 588) → pair (102, 588)
28. 119 divides 59976 (59976 ÷ 119 = 504) → pair (119, 504)
29. 126 divides 59976 (59976 ÷ 126 = 476) → pair (126, 476)
30. 136 divides 59976 (59976 ÷ 136 = 441) → pair (136, 441)
31. 147 divides 59976 (59976 ÷ 147 = 408) → pair (147, 408)
32. 153 divides 59976 (59976 ÷ 153 = 392) → pair (153, 392)
33. 168 divides 59976 (59976 ÷ 168 = 357) → pair (168, 357)
34. 196 divides 59976 (59976 ÷ 196 = 306) → pair (196, 306)
35. 204 divides 59976 (59976 ÷ 204 = 294) → pair (204, 294)
36. 238 divides 59976 (59976 ÷ 238 = 252) → pair (238, 252)
37. Collect all unique values: {1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 17, 18, 21, 24, 28, 34, 36, 42, 49, 51, 56, 63, 68, 72, 84, 98, 102, 119, 126, 136, 147, 153, 168, 196, 204, 238, 252, 294, 306, 357, 392, 408, 441, 476, 504, 588, 612, 714, 833, 882, 952, 1071, 1176, 1224, 1428, 1666, 1764, 2142, 2499, 2856, 3332, 3528, 4284, 4998, 6664, 7497, 8568, 9996, 14994, 19992, 29988, 59976} — total 72 divisors.
38. Sum: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 17 + 18 + 21 + 24 + 28 + 34 + 36 + 42 + 49 + 51 + 56 + 63 + 68 + 72 + 84 + 98 + 102 + 119 + 126 + 136 + 147 + 153 + 168 + 196 + 204 + 238 + 252 + 294 + 306 + 357 + 392 + 408 + 441 + 476 + 504 + 588 + 612 + 714 + 833 + 882 + 952 + 1071 + 1176 + 1224 + 1428 + 1666 + 1764 + 2142 + 2499 + 2856 + 3332 + 3528 + 4284 + 4998 + 6664 + 7497 + 8568 + 9996 + 14994 + 19992 + 29988 + 59976 = 200070.

Nearby Examples

Related Operations for 59976

• Multiples of a Number — "outward" complement of divisors
• 59976 Prime Factorization — decompose into prime building blocks
• Find GCF of 59976 and another number
• Find LCM of 59976 and another number
• Is 59976 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

Find all divisors of these numbers: