Divisors of 1680: 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 1680

The number 1680 has 40 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  16,  20,  21,  24,  28,  30,  35,  40,  42,  48,  56,  60,  70,  80,  84,  105,  112,  120,  140,  168,  210,  240,  280,  336,  420,  560,  840,  1680

Divisor Pairs of 1680

Each pair multiplies to 1680:

Number of Divisors

The number 1680 has 40 divisors, written as τ(1680) = 40 in number theory.

Sum of Divisors

σ(1680) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 28 + 30 + 35 + 40 + 42 + 48 + 56 + 60 + 70 + 80 + 84 + 105 + 112 + 120 + 140 + 168 + 210 + 240 + 280 + 336 + 420 + 560 + 840 + 1680 = 5952

Prime Factorization of 1680

See the full prime factorization calculator →

Properties of 1680

• 1680 is composite.
• 1680 is not a perfect square.
• Number of divisors: 40.
• Sum of divisors: 5952.

Common Divisors with Another Number?

Looking for the divisors that 1680 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 1680

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √1680 ≈ 40.99. If i divides 1680, then both i and 1680/i are divisors.

1. 1 divides 1680 (1680 ÷ 1 = 1680) → pair (1, 1680)
2. 2 divides 1680 (1680 ÷ 2 = 840) → pair (2, 840)
3. 3 divides 1680 (1680 ÷ 3 = 560) → pair (3, 560)
4. 4 divides 1680 (1680 ÷ 4 = 420) → pair (4, 420)
5. 5 divides 1680 (1680 ÷ 5 = 336) → pair (5, 336)
6. 6 divides 1680 (1680 ÷ 6 = 280) → pair (6, 280)
7. 7 divides 1680 (1680 ÷ 7 = 240) → pair (7, 240)
8. 8 divides 1680 (1680 ÷ 8 = 210) → pair (8, 210)
9. 10 divides 1680 (1680 ÷ 10 = 168) → pair (10, 168)
10. 12 divides 1680 (1680 ÷ 12 = 140) → pair (12, 140)
11. 14 divides 1680 (1680 ÷ 14 = 120) → pair (14, 120)
12. 15 divides 1680 (1680 ÷ 15 = 112) → pair (15, 112)
13. 16 divides 1680 (1680 ÷ 16 = 105) → pair (16, 105)
14. 20 divides 1680 (1680 ÷ 20 = 84) → pair (20, 84)
15. 21 divides 1680 (1680 ÷ 21 = 80) → pair (21, 80)
16. 24 divides 1680 (1680 ÷ 24 = 70) → pair (24, 70)
17. 28 divides 1680 (1680 ÷ 28 = 60) → pair (28, 60)
18. 30 divides 1680 (1680 ÷ 30 = 56) → pair (30, 56)
19. 35 divides 1680 (1680 ÷ 35 = 48) → pair (35, 48)
20. 40 divides 1680 (1680 ÷ 40 = 42) → pair (40, 42)
21. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680} — total 40 divisors.
22. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 28 + 30 + 35 + 40 + 42 + 48 + 56 + 60 + 70 + 80 + 84 + 105 + 112 + 120 + 140 + 168 + 210 + 240 + 280 + 336 + 420 + 560 + 840 + 1680 = 5952.

Nearby Examples

Related Operations for 1680

• Multiples of 1680 — "outward" complement; M is a multiple of 1680 ⇔ 1680 is a divisor of M
• 1680 Prime Factorization — decompose into prime building blocks
• Find GCF of 1680 and another number
• Find LCM of 1680 and another number
• Is 1680 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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