Divisors of 77976: 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 77976

The number 77976 has 48 divisors:

1,  2,  3,  4,  6,  8,  9,  12,  18,  19,  24,  27,  36,  38,  54,  57,  72,  76,  108,  114,  152,  171,  216,  228,  342,  361,  456,  513,  684,  722,  1026,  1083,  1368,  1444,  2052,  2166,  2888,  3249,  4104,  4332,  6498,  8664,  9747,  12996,  19494,  25992,  38988,  77976

Divisor Pairs of 77976

Each pair multiplies to 77976:

Number of Divisors

The number 77976 has 48 divisors, written as τ(77976) = 48 in number theory.

Sum of Divisors

σ(77976) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 19 + 24 + 27 + 36 + 38 + 54 + 57 + 72 + 76 + 108 + 114 + 152 + 171 + 216 + 228 + 342 + 361 + 456 + 513 + 684 + 722 + 1026 + 1083 + 1368 + 1444 + 2052 + 2166 + 2888 + 3249 + 4104 + 4332 + 6498 + 8664 + 9747 + 12996 + 19494 + 25992 + 38988 + 77976 = 228600

Prime Factorization of 77976

See the full prime factorization calculator →

Properties of 77976

• 77976 is composite.
• 77976 is not a perfect square.
• Number of divisors: 48.
• Sum of divisors: 228600.

Common Divisors with Another Number?

Looking for the divisors that 77976 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 77976

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √77976 ≈ 279.24. If i divides 77976, then both i and 77976/i are divisors.

1. 1 divides 77976 (77976 ÷ 1 = 77976) → pair (1, 77976)
2. 2 divides 77976 (77976 ÷ 2 = 38988) → pair (2, 38988)
3. 3 divides 77976 (77976 ÷ 3 = 25992) → pair (3, 25992)
4. 4 divides 77976 (77976 ÷ 4 = 19494) → pair (4, 19494)
5. 6 divides 77976 (77976 ÷ 6 = 12996) → pair (6, 12996)
6. 8 divides 77976 (77976 ÷ 8 = 9747) → pair (8, 9747)
7. 9 divides 77976 (77976 ÷ 9 = 8664) → pair (9, 8664)
8. 12 divides 77976 (77976 ÷ 12 = 6498) → pair (12, 6498)
9. 18 divides 77976 (77976 ÷ 18 = 4332) → pair (18, 4332)
10. 19 divides 77976 (77976 ÷ 19 = 4104) → pair (19, 4104)
11. 24 divides 77976 (77976 ÷ 24 = 3249) → pair (24, 3249)
12. 27 divides 77976 (77976 ÷ 27 = 2888) → pair (27, 2888)
13. 36 divides 77976 (77976 ÷ 36 = 2166) → pair (36, 2166)
14. 38 divides 77976 (77976 ÷ 38 = 2052) → pair (38, 2052)
15. 54 divides 77976 (77976 ÷ 54 = 1444) → pair (54, 1444)
16. 57 divides 77976 (77976 ÷ 57 = 1368) → pair (57, 1368)
17. 72 divides 77976 (77976 ÷ 72 = 1083) → pair (72, 1083)
18. 76 divides 77976 (77976 ÷ 76 = 1026) → pair (76, 1026)
19. 108 divides 77976 (77976 ÷ 108 = 722) → pair (108, 722)
20. 114 divides 77976 (77976 ÷ 114 = 684) → pair (114, 684)
21. 152 divides 77976 (77976 ÷ 152 = 513) → pair (152, 513)
22. 171 divides 77976 (77976 ÷ 171 = 456) → pair (171, 456)
23. 216 divides 77976 (77976 ÷ 216 = 361) → pair (216, 361)
24. 228 divides 77976 (77976 ÷ 228 = 342) → pair (228, 342)
25. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 27, 36, 38, 54, 57, 72, 76, 108, 114, 152, 171, 216, 228, 342, 361, 456, 513, 684, 722, 1026, 1083, 1368, 1444, 2052, 2166, 2888, 3249, 4104, 4332, 6498, 8664, 9747, 12996, 19494, 25992, 38988, 77976} — total 48 divisors.
26. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 19 + 24 + 27 + 36 + 38 + 54 + 57 + 72 + 76 + 108 + 114 + 152 + 171 + 216 + 228 + 342 + 361 + 456 + 513 + 684 + 722 + 1026 + 1083 + 1368 + 1444 + 2052 + 2166 + 2888 + 3249 + 4104 + 4332 + 6498 + 8664 + 9747 + 12996 + 19494 + 25992 + 38988 + 77976 = 228600.

Nearby Examples

Related Operations for 77976

• Multiples of a Number — "outward" complement of divisors
• 77976 Prime Factorization — decompose into prime building blocks
• Find GCF of 77976 and another number
• Find LCM of 77976 and another number
• Is 77976 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: