Divisors of 37680: All 40 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 37680

The number 37680 has 40 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  16,  20,  24,  30,  40,  48,  60,  80,  120,  157,  240,  314,  471,  628,  785,  942,  1256,  1570,  1884,  2355,  2512,  3140,  3768,  4710,  6280,  7536,  9420,  12560,  18840,  37680

Divisor Pairs of 37680

Each pair multiplies to 37680:

Number of Divisors

The number 37680 has 40 divisors, written as τ(37680) = 40 in number theory.

Sum of Divisors

σ(37680) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 40 + 48 + 60 + 80 + 120 + 157 + 240 + 314 + 471 + 628 + 785 + 942 + 1256 + 1570 + 1884 + 2355 + 2512 + 3140 + 3768 + 4710 + 6280 + 7536 + 9420 + 12560 + 18840 + 37680 = 117552

Prime Factorization of 37680

See the full prime factorization calculator →

Properties of 37680

• 37680 is composite.
• 37680 is not a perfect square.
• Number of divisors: 40.
• Sum of divisors: 117552.

Common Divisors with Another Number?

Looking for the divisors that 37680 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 37680

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √37680 ≈ 194.11. If i divides 37680, then both i and 37680/i are divisors.

1. 1 divides 37680 (37680 ÷ 1 = 37680) → pair (1, 37680)
2. 2 divides 37680 (37680 ÷ 2 = 18840) → pair (2, 18840)
3. 3 divides 37680 (37680 ÷ 3 = 12560) → pair (3, 12560)
4. 4 divides 37680 (37680 ÷ 4 = 9420) → pair (4, 9420)
5. 5 divides 37680 (37680 ÷ 5 = 7536) → pair (5, 7536)
6. 6 divides 37680 (37680 ÷ 6 = 6280) → pair (6, 6280)
7. 8 divides 37680 (37680 ÷ 8 = 4710) → pair (8, 4710)
8. 10 divides 37680 (37680 ÷ 10 = 3768) → pair (10, 3768)
9. 12 divides 37680 (37680 ÷ 12 = 3140) → pair (12, 3140)
10. 15 divides 37680 (37680 ÷ 15 = 2512) → pair (15, 2512)
11. 16 divides 37680 (37680 ÷ 16 = 2355) → pair (16, 2355)
12. 20 divides 37680 (37680 ÷ 20 = 1884) → pair (20, 1884)
13. 24 divides 37680 (37680 ÷ 24 = 1570) → pair (24, 1570)
14. 30 divides 37680 (37680 ÷ 30 = 1256) → pair (30, 1256)
15. 40 divides 37680 (37680 ÷ 40 = 942) → pair (40, 942)
16. 48 divides 37680 (37680 ÷ 48 = 785) → pair (48, 785)
17. 60 divides 37680 (37680 ÷ 60 = 628) → pair (60, 628)
18. 80 divides 37680 (37680 ÷ 80 = 471) → pair (80, 471)
19. 120 divides 37680 (37680 ÷ 120 = 314) → pair (120, 314)
20. 157 divides 37680 (37680 ÷ 157 = 240) → pair (157, 240)
21. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 157, 240, 314, 471, 628, 785, 942, 1256, 1570, 1884, 2355, 2512, 3140, 3768, 4710, 6280, 7536, 9420, 12560, 18840, 37680} — total 40 divisors.
22. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 40 + 48 + 60 + 80 + 120 + 157 + 240 + 314 + 471 + 628 + 785 + 942 + 1256 + 1570 + 1884 + 2355 + 2512 + 3140 + 3768 + 4710 + 6280 + 7536 + 9420 + 12560 + 18840 + 37680 = 117552.

Nearby Examples

Related Operations for 37680

• Multiples of a Number — "outward" complement of divisors
• 37680 Prime Factorization — decompose into prime building blocks
• Find GCF of 37680 and another number
• Find LCM of 37680 and another number
• Is 37680 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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