Divisors of 8040: All 32 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 8040

The number 8040 has 32 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  20,  24,  30,  40,  60,  67,  120,  134,  201,  268,  335,  402,  536,  670,  804,  1005,  1340,  1608,  2010,  2680,  4020,  8040

Divisor Pairs of 8040

Each pair multiplies to 8040:

Number of Divisors

The number 8040 has 32 divisors, written as τ(8040) = 32 in number theory.

Sum of Divisors

σ(8040) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 + 67 + 120 + 134 + 201 + 268 + 335 + 402 + 536 + 670 + 804 + 1005 + 1340 + 1608 + 2010 + 2680 + 4020 + 8040 = 24480

Prime Factorization of 8040

See the full prime factorization calculator →

Properties of 8040

• 8040 is composite.
• 8040 is not a perfect square.
• Number of divisors: 32.
• Sum of divisors: 24480.

Common Divisors with Another Number?

Looking for the divisors that 8040 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 8040

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √8040 ≈ 89.67. If i divides 8040, then both i and 8040/i are divisors.

1. 1 divides 8040 (8040 ÷ 1 = 8040) → pair (1, 8040)
2. 2 divides 8040 (8040 ÷ 2 = 4020) → pair (2, 4020)
3. 3 divides 8040 (8040 ÷ 3 = 2680) → pair (3, 2680)
4. 4 divides 8040 (8040 ÷ 4 = 2010) → pair (4, 2010)
5. 5 divides 8040 (8040 ÷ 5 = 1608) → pair (5, 1608)
6. 6 divides 8040 (8040 ÷ 6 = 1340) → pair (6, 1340)
7. 8 divides 8040 (8040 ÷ 8 = 1005) → pair (8, 1005)
8. 10 divides 8040 (8040 ÷ 10 = 804) → pair (10, 804)
9. 12 divides 8040 (8040 ÷ 12 = 670) → pair (12, 670)
10. 15 divides 8040 (8040 ÷ 15 = 536) → pair (15, 536)
11. 20 divides 8040 (8040 ÷ 20 = 402) → pair (20, 402)
12. 24 divides 8040 (8040 ÷ 24 = 335) → pair (24, 335)
13. 30 divides 8040 (8040 ÷ 30 = 268) → pair (30, 268)
14. 40 divides 8040 (8040 ÷ 40 = 201) → pair (40, 201)
15. 60 divides 8040 (8040 ÷ 60 = 134) → pair (60, 134)
16. 67 divides 8040 (8040 ÷ 67 = 120) → pair (67, 120)
17. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 67, 120, 134, 201, 268, 335, 402, 536, 670, 804, 1005, 1340, 1608, 2010, 2680, 4020, 8040} — total 32 divisors.
18. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 + 67 + 120 + 134 + 201 + 268 + 335 + 402 + 536 + 670 + 804 + 1005 + 1340 + 1608 + 2010 + 2680 + 4020 + 8040 = 24480.

Nearby Examples

Related Operations for 8040

• Multiples of 8040 — "outward" complement; M is a multiple of 8040 ⇔ 8040 is a divisor of M
• 8040 Prime Factorization — decompose into prime building blocks
• Find GCF of 8040 and another number
• Find LCM of 8040 and another number
• Is 8040 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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