Divisors of 5040: 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 5040

The number 5040 has 60 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  12,  14,  15,  16,  18,  20,  21,  24,  28,  30,  35,  36,  40,  42,  45,  48,  56,  60,  63,  70,  72,  80,  84,  90,  105,  112,  120,  126,  140,  144,  168,  180,  210,  240,  252,  280,  315,  336,  360,  420,  504,  560,  630,  720,  840,  1008,  1260,  1680,  2520,  5040

Divisor Pairs of 5040

Each pair multiplies to 5040:

Number of Divisors

The number 5040 has 60 divisors, written as τ(5040) = 60 in number theory.

Sum of Divisors

σ(5040) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 28 + 30 + 35 + 36 + 40 + 42 + 45 + 48 + 56 + 60 + 63 + 70 + 72 + 80 + 84 + 90 + 105 + 112 + 120 + 126 + 140 + 144 + 168 + 180 + 210 + 240 + 252 + 280 + 315 + 336 + 360 + 420 + 504 + 560 + 630 + 720 + 840 + 1008 + 1260 + 1680 + 2520 + 5040 = 19344

Prime Factorization of 5040

See the full prime factorization calculator →

Properties of 5040

• 5040 is composite.
• 5040 is not a perfect square.
• Number of divisors: 60.
• Sum of divisors: 19344.

Common Divisors with Another Number?

Looking for the divisors that 5040 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 5040

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √5040 ≈ 70.99. If i divides 5040, then both i and 5040/i are divisors.

1. 1 divides 5040 (5040 ÷ 1 = 5040) → pair (1, 5040)
2. 2 divides 5040 (5040 ÷ 2 = 2520) → pair (2, 2520)
3. 3 divides 5040 (5040 ÷ 3 = 1680) → pair (3, 1680)
4. 4 divides 5040 (5040 ÷ 4 = 1260) → pair (4, 1260)
5. 5 divides 5040 (5040 ÷ 5 = 1008) → pair (5, 1008)
6. 6 divides 5040 (5040 ÷ 6 = 840) → pair (6, 840)
7. 7 divides 5040 (5040 ÷ 7 = 720) → pair (7, 720)
8. 8 divides 5040 (5040 ÷ 8 = 630) → pair (8, 630)
9. 9 divides 5040 (5040 ÷ 9 = 560) → pair (9, 560)
10. 10 divides 5040 (5040 ÷ 10 = 504) → pair (10, 504)
11. 12 divides 5040 (5040 ÷ 12 = 420) → pair (12, 420)
12. 14 divides 5040 (5040 ÷ 14 = 360) → pair (14, 360)
13. 15 divides 5040 (5040 ÷ 15 = 336) → pair (15, 336)
14. 16 divides 5040 (5040 ÷ 16 = 315) → pair (16, 315)
15. 18 divides 5040 (5040 ÷ 18 = 280) → pair (18, 280)
16. 20 divides 5040 (5040 ÷ 20 = 252) → pair (20, 252)
17. 21 divides 5040 (5040 ÷ 21 = 240) → pair (21, 240)
18. 24 divides 5040 (5040 ÷ 24 = 210) → pair (24, 210)
19. 28 divides 5040 (5040 ÷ 28 = 180) → pair (28, 180)
20. 30 divides 5040 (5040 ÷ 30 = 168) → pair (30, 168)
21. 35 divides 5040 (5040 ÷ 35 = 144) → pair (35, 144)
22. 36 divides 5040 (5040 ÷ 36 = 140) → pair (36, 140)
23. 40 divides 5040 (5040 ÷ 40 = 126) → pair (40, 126)
24. 42 divides 5040 (5040 ÷ 42 = 120) → pair (42, 120)
25. 45 divides 5040 (5040 ÷ 45 = 112) → pair (45, 112)
26. 48 divides 5040 (5040 ÷ 48 = 105) → pair (48, 105)
27. 56 divides 5040 (5040 ÷ 56 = 90) → pair (56, 90)
28. 60 divides 5040 (5040 ÷ 60 = 84) → pair (60, 84)
29. 63 divides 5040 (5040 ÷ 63 = 80) → pair (63, 80)
30. 70 divides 5040 (5040 ÷ 70 = 72) → pair (70, 72)
31. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040} — total 60 divisors.
32. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 28 + 30 + 35 + 36 + 40 + 42 + 45 + 48 + 56 + 60 + 63 + 70 + 72 + 80 + 84 + 90 + 105 + 112 + 120 + 126 + 140 + 144 + 168 + 180 + 210 + 240 + 252 + 280 + 315 + 336 + 360 + 420 + 504 + 560 + 630 + 720 + 840 + 1008 + 1260 + 1680 + 2520 + 5040 = 19344.

Nearby Examples

Related Operations for 5040

• Multiples of 5040 — "outward" complement; M is a multiple of 5040 ⇔ 5040 is a divisor of M
• 5040 Prime Factorization — decompose into prime building blocks
• Find GCF of 5040 and another number
• Find LCM of 5040 and another number
• Is 5040 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: