Divisors of 3136: All 21 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 3136

The number 3136 has 21 divisors:

1,  2,  4,  7,  8,  14,  16,  28,  32,  49,  56,  64,  98,  112,  196,  224,  392,  448,  784,  1568,  3136

Divisor Pairs of 3136

Each pair multiplies to 3136:

Note: the last pair has identical factors (56 × 56) because 3136 is a perfect square.

Number of Divisors

The number 3136 has 21 divisors, written as τ(3136) = 21 in number theory.

⚡ Notice: 3136 has an odd number of divisors — this means 3136 is a perfect square (√3136 = 56).

Sum of Divisors

σ(3136) = 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 32 + 49 + 56 + 64 + 98 + 112 + 196 + 224 + 392 + 448 + 784 + 1568 + 3136 = 7239

Prime Factorization of 3136

See the full prime factorization calculator →

Properties of 3136

• 3136 is composite.
• 3136 is a perfect square (√3136 = 56).
• Number of divisors: 21.
• Sum of divisors: 7239.

Common Divisors with Another Number?

Looking for the divisors that 3136 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 3136

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √3136 ≈ 56.00. If i divides 3136, then both i and 3136/i are divisors.

1. 1 divides 3136 (3136 ÷ 1 = 3136) → pair (1, 3136)
2. 2 divides 3136 (3136 ÷ 2 = 1568) → pair (2, 1568)
3. 4 divides 3136 (3136 ÷ 4 = 784) → pair (4, 784)
4. 7 divides 3136 (3136 ÷ 7 = 448) → pair (7, 448)
5. 8 divides 3136 (3136 ÷ 8 = 392) → pair (8, 392)
6. 14 divides 3136 (3136 ÷ 14 = 224) → pair (14, 224)
7. 16 divides 3136 (3136 ÷ 16 = 196) → pair (16, 196)
8. 28 divides 3136 (3136 ÷ 28 = 112) → pair (28, 112)
9. 32 divides 3136 (3136 ÷ 32 = 98) → pair (32, 98)
10. 49 divides 3136 (3136 ÷ 49 = 64) → pair (49, 64)
11. 56 divides 3136 (3136 ÷ 56 = 56) → pair (56, 56)
12. Collect all unique values: {1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136} — total 21 divisors.
13. Sum: 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 32 + 49 + 56 + 64 + 98 + 112 + 196 + 224 + 392 + 448 + 784 + 1568 + 3136 = 7239.

Nearby Examples

Related Operations for 3136

• Multiples of 3136 — "outward" complement; M is a multiple of 3136 ⇔ 3136 is a divisor of M
• 3136 Prime Factorization — decompose into prime building blocks
• Find GCF of 3136 and another number
• Find LCM of 3136 and another number
• Is 3136 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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