Divisors of 2142: All 24 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 2142

The number 2142 has 24 divisors:

1,  2,  3,  6,  7,  9,  14,  17,  18,  21,  34,  42,  51,  63,  102,  119,  126,  153,  238,  306,  357,  714,  1071,  2142

Divisor Pairs of 2142

Each pair multiplies to 2142:

Number of Divisors

The number 2142 has 24 divisors, written as τ(2142) = 24 in number theory.

Sum of Divisors

σ(2142) = 1 + 2 + 3 + 6 + 7 + 9 + 14 + 17 + 18 + 21 + 34 + 42 + 51 + 63 + 102 + 119 + 126 + 153 + 238 + 306 + 357 + 714 + 1071 + 2142 = 5616

Prime Factorization of 2142

See the full prime factorization calculator →

Properties of 2142

• 2142 is composite.
• 2142 is not a perfect square.
• Number of divisors: 24.
• Sum of divisors: 5616.

Common Divisors with Another Number?

Looking for the divisors that 2142 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 2142

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √2142 ≈ 46.28. If i divides 2142, then both i and 2142/i are divisors.

1. 1 divides 2142 (2142 ÷ 1 = 2142) → pair (1, 2142)
2. 2 divides 2142 (2142 ÷ 2 = 1071) → pair (2, 1071)
3. 3 divides 2142 (2142 ÷ 3 = 714) → pair (3, 714)
4. 6 divides 2142 (2142 ÷ 6 = 357) → pair (6, 357)
5. 7 divides 2142 (2142 ÷ 7 = 306) → pair (7, 306)
6. 9 divides 2142 (2142 ÷ 9 = 238) → pair (9, 238)
7. 14 divides 2142 (2142 ÷ 14 = 153) → pair (14, 153)
8. 17 divides 2142 (2142 ÷ 17 = 126) → pair (17, 126)
9. 18 divides 2142 (2142 ÷ 18 = 119) → pair (18, 119)
10. 21 divides 2142 (2142 ÷ 21 = 102) → pair (21, 102)
11. 34 divides 2142 (2142 ÷ 34 = 63) → pair (34, 63)
12. 42 divides 2142 (2142 ÷ 42 = 51) → pair (42, 51)
13. Collect all unique values: {1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071, 2142} — total 24 divisors.
14. Sum: 1 + 2 + 3 + 6 + 7 + 9 + 14 + 17 + 18 + 21 + 34 + 42 + 51 + 63 + 102 + 119 + 126 + 153 + 238 + 306 + 357 + 714 + 1071 + 2142 = 5616.

Nearby Examples

Related Operations for 2142

• Multiples of 2142 — "outward" complement; M is a multiple of 2142 ⇔ 2142 is a divisor of M
• 2142 Prime Factorization — decompose into prime building blocks
• Find GCF of 2142 and another number
• Find LCM of 2142 and another number
• Is 2142 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)

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