Divisors of 59940: All 60 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 59940

The number 59940 has 60 divisors:

1,  2,  3,  4,  5,  6,  9,  10,  12,  15,  18,  20,  27,  30,  36,  37,  45,  54,  60,  74,  81,  90,  108,  111,  135,  148,  162,  180,  185,  222,  270,  324,  333,  370,  405,  444,  540,  555,  666,  740,  810,  999,  1110,  1332,  1620,  1665,  1998,  2220,  2997,  3330,  3996,  4995,  5994,  6660,  9990,  11988,  14985,  19980,  29970,  59940

Divisor Pairs of 59940

Each pair multiplies to 59940:

Number of Divisors

The number 59940 has 60 divisors, written as τ(59940) = 60 in number theory.

Sum of Divisors

σ(59940) = 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 27 + 30 + 36 + 37 + 45 + 54 + 60 + 74 + 81 + 90 + 108 + 111 + 135 + 148 + 162 + 180 + 185 + 222 + 270 + 324 + 333 + 370 + 405 + 444 + 540 + 555 + 666 + 740 + 810 + 999 + 1110 + 1332 + 1620 + 1665 + 1998 + 2220 + 2997 + 3330 + 3996 + 4995 + 5994 + 6660 + 9990 + 11988 + 14985 + 19980 + 29970 + 59940 = 193116

Prime Factorization of 59940

See the full prime factorization calculator →

Properties of 59940

• 59940 is composite.
• 59940 is not a perfect square.
• Number of divisors: 60.
• Sum of divisors: 193116.

Common Divisors with Another Number?

Looking for the divisors that 59940 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 59940

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √59940 ≈ 244.83. If i divides 59940, then both i and 59940/i are divisors.

1. 1 divides 59940 (59940 ÷ 1 = 59940) → pair (1, 59940)
2. 2 divides 59940 (59940 ÷ 2 = 29970) → pair (2, 29970)
3. 3 divides 59940 (59940 ÷ 3 = 19980) → pair (3, 19980)
4. 4 divides 59940 (59940 ÷ 4 = 14985) → pair (4, 14985)
5. 5 divides 59940 (59940 ÷ 5 = 11988) → pair (5, 11988)
6. 6 divides 59940 (59940 ÷ 6 = 9990) → pair (6, 9990)
7. 9 divides 59940 (59940 ÷ 9 = 6660) → pair (9, 6660)
8. 10 divides 59940 (59940 ÷ 10 = 5994) → pair (10, 5994)
9. 12 divides 59940 (59940 ÷ 12 = 4995) → pair (12, 4995)
10. 15 divides 59940 (59940 ÷ 15 = 3996) → pair (15, 3996)
11. 18 divides 59940 (59940 ÷ 18 = 3330) → pair (18, 3330)
12. 20 divides 59940 (59940 ÷ 20 = 2997) → pair (20, 2997)
13. 27 divides 59940 (59940 ÷ 27 = 2220) → pair (27, 2220)
14. 30 divides 59940 (59940 ÷ 30 = 1998) → pair (30, 1998)
15. 36 divides 59940 (59940 ÷ 36 = 1665) → pair (36, 1665)
16. 37 divides 59940 (59940 ÷ 37 = 1620) → pair (37, 1620)
17. 45 divides 59940 (59940 ÷ 45 = 1332) → pair (45, 1332)
18. 54 divides 59940 (59940 ÷ 54 = 1110) → pair (54, 1110)
19. 60 divides 59940 (59940 ÷ 60 = 999) → pair (60, 999)
20. 74 divides 59940 (59940 ÷ 74 = 810) → pair (74, 810)
21. 81 divides 59940 (59940 ÷ 81 = 740) → pair (81, 740)
22. 90 divides 59940 (59940 ÷ 90 = 666) → pair (90, 666)
23. 108 divides 59940 (59940 ÷ 108 = 555) → pair (108, 555)
24. 111 divides 59940 (59940 ÷ 111 = 540) → pair (111, 540)
25. 135 divides 59940 (59940 ÷ 135 = 444) → pair (135, 444)
26. 148 divides 59940 (59940 ÷ 148 = 405) → pair (148, 405)
27. 162 divides 59940 (59940 ÷ 162 = 370) → pair (162, 370)
28. 180 divides 59940 (59940 ÷ 180 = 333) → pair (180, 333)
29. 185 divides 59940 (59940 ÷ 185 = 324) → pair (185, 324)
30. 222 divides 59940 (59940 ÷ 222 = 270) → pair (222, 270)
31. Collect all unique values: {1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 37, 45, 54, 60, 74, 81, 90, 108, 111, 135, 148, 162, 180, 185, 222, 270, 324, 333, 370, 405, 444, 540, 555, 666, 740, 810, 999, 1110, 1332, 1620, 1665, 1998, 2220, 2997, 3330, 3996, 4995, 5994, 6660, 9990, 11988, 14985, 19980, 29970, 59940} — total 60 divisors.
32. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 27 + 30 + 36 + 37 + 45 + 54 + 60 + 74 + 81 + 90 + 108 + 111 + 135 + 148 + 162 + 180 + 185 + 222 + 270 + 324 + 333 + 370 + 405 + 444 + 540 + 555 + 666 + 740 + 810 + 999 + 1110 + 1332 + 1620 + 1665 + 1998 + 2220 + 2997 + 3330 + 3996 + 4995 + 5994 + 6660 + 9990 + 11988 + 14985 + 19980 + 29970 + 59940 = 193116.

Nearby Examples

Related Operations for 59940

• Multiples of a Number — "outward" complement of divisors
• 59940 Prime Factorization — decompose into prime building blocks
• Find GCF of 59940 and another number
• Find LCM of 59940 and another number
• Is 59940 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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