Divisors of 39960: All 64 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 39960

The number 39960 has 64 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  18,  20,  24,  27,  30,  36,  37,  40,  45,  54,  60,  72,  74,  90,  108,  111,  120,  135,  148,  180,  185,  216,  222,  270,  296,  333,  360,  370,  444,  540,  555,  666,  740,  888,  999,  1080,  1110,  1332,  1480,  1665,  1998,  2220,  2664,  3330,  3996,  4440,  4995,  6660,  7992,  9990,  13320,  19980,  39960

Divisor Pairs of 39960

Each pair multiplies to 39960:

Number of Divisors

The number 39960 has 64 divisors, written as τ(39960) = 64 in number theory.

Sum of Divisors

σ(39960) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 27 + 30 + 36 + 37 + 40 + 45 + 54 + 60 + 72 + 74 + 90 + 108 + 111 + 120 + 135 + 148 + 180 + 185 + 216 + 222 + 270 + 296 + 333 + 360 + 370 + 444 + 540 + 555 + 666 + 740 + 888 + 999 + 1080 + 1110 + 1332 + 1480 + 1665 + 1998 + 2220 + 2664 + 3330 + 3996 + 4440 + 4995 + 6660 + 7992 + 9990 + 13320 + 19980 + 39960 = 136800

Prime Factorization of 39960

See the full prime factorization calculator →

Properties of 39960

• 39960 is composite.
• 39960 is not a perfect square.
• Number of divisors: 64.
• Sum of divisors: 136800.

Common Divisors with Another Number?

Looking for the divisors that 39960 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 39960

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √39960 ≈ 199.90. If i divides 39960, then both i and 39960/i are divisors.

1. 1 divides 39960 (39960 ÷ 1 = 39960) → pair (1, 39960)
2. 2 divides 39960 (39960 ÷ 2 = 19980) → pair (2, 19980)
3. 3 divides 39960 (39960 ÷ 3 = 13320) → pair (3, 13320)
4. 4 divides 39960 (39960 ÷ 4 = 9990) → pair (4, 9990)
5. 5 divides 39960 (39960 ÷ 5 = 7992) → pair (5, 7992)
6. 6 divides 39960 (39960 ÷ 6 = 6660) → pair (6, 6660)
7. 8 divides 39960 (39960 ÷ 8 = 4995) → pair (8, 4995)
8. 9 divides 39960 (39960 ÷ 9 = 4440) → pair (9, 4440)
9. 10 divides 39960 (39960 ÷ 10 = 3996) → pair (10, 3996)
10. 12 divides 39960 (39960 ÷ 12 = 3330) → pair (12, 3330)
11. 15 divides 39960 (39960 ÷ 15 = 2664) → pair (15, 2664)
12. 18 divides 39960 (39960 ÷ 18 = 2220) → pair (18, 2220)
13. 20 divides 39960 (39960 ÷ 20 = 1998) → pair (20, 1998)
14. 24 divides 39960 (39960 ÷ 24 = 1665) → pair (24, 1665)
15. 27 divides 39960 (39960 ÷ 27 = 1480) → pair (27, 1480)
16. 30 divides 39960 (39960 ÷ 30 = 1332) → pair (30, 1332)
17. 36 divides 39960 (39960 ÷ 36 = 1110) → pair (36, 1110)
18. 37 divides 39960 (39960 ÷ 37 = 1080) → pair (37, 1080)
19. 40 divides 39960 (39960 ÷ 40 = 999) → pair (40, 999)
20. 45 divides 39960 (39960 ÷ 45 = 888) → pair (45, 888)
21. 54 divides 39960 (39960 ÷ 54 = 740) → pair (54, 740)
22. 60 divides 39960 (39960 ÷ 60 = 666) → pair (60, 666)
23. 72 divides 39960 (39960 ÷ 72 = 555) → pair (72, 555)
24. 74 divides 39960 (39960 ÷ 74 = 540) → pair (74, 540)
25. 90 divides 39960 (39960 ÷ 90 = 444) → pair (90, 444)
26. 108 divides 39960 (39960 ÷ 108 = 370) → pair (108, 370)
27. 111 divides 39960 (39960 ÷ 111 = 360) → pair (111, 360)
28. 120 divides 39960 (39960 ÷ 120 = 333) → pair (120, 333)
29. 135 divides 39960 (39960 ÷ 135 = 296) → pair (135, 296)
30. 148 divides 39960 (39960 ÷ 148 = 270) → pair (148, 270)
31. 180 divides 39960 (39960 ÷ 180 = 222) → pair (180, 222)
32. 185 divides 39960 (39960 ÷ 185 = 216) → pair (185, 216)
33. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 37, 40, 45, 54, 60, 72, 74, 90, 108, 111, 120, 135, 148, 180, 185, 216, 222, 270, 296, 333, 360, 370, 444, 540, 555, 666, 740, 888, 999, 1080, 1110, 1332, 1480, 1665, 1998, 2220, 2664, 3330, 3996, 4440, 4995, 6660, 7992, 9990, 13320, 19980, 39960} — total 64 divisors.
34. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 27 + 30 + 36 + 37 + 40 + 45 + 54 + 60 + 72 + 74 + 90 + 108 + 111 + 120 + 135 + 148 + 180 + 185 + 216 + 222 + 270 + 296 + 333 + 360 + 370 + 444 + 540 + 555 + 666 + 740 + 888 + 999 + 1080 + 1110 + 1332 + 1480 + 1665 + 1998 + 2220 + 2664 + 3330 + 3996 + 4440 + 4995 + 6660 + 7992 + 9990 + 13320 + 19980 + 39960 = 136800.

Nearby Examples

Related Operations for 39960

• Multiples of a Number — "outward" complement of divisors
• 39960 Prime Factorization — decompose into prime building blocks
• Find GCF of 39960 and another number
• Find LCM of 39960 and another number
• Is 39960 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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