Divisors of 9984: All 36 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 9984

The number 9984 has 36 divisors:

1,  2,  3,  4,  6,  8,  12,  13,  16,  24,  26,  32,  39,  48,  52,  64,  78,  96,  104,  128,  156,  192,  208,  256,  312,  384,  416,  624,  768,  832,  1248,  1664,  2496,  3328,  4992,  9984

Divisor Pairs of 9984

Each pair multiplies to 9984:

Number of Divisors

The number 9984 has 36 divisors, written as τ(9984) = 36 in number theory.

Sum of Divisors

σ(9984) = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 16 + 24 + 26 + 32 + 39 + 48 + 52 + 64 + 78 + 96 + 104 + 128 + 156 + 192 + 208 + 256 + 312 + 384 + 416 + 624 + 768 + 832 + 1248 + 1664 + 2496 + 3328 + 4992 + 9984 = 28616

Prime Factorization of 9984

See the full prime factorization calculator →

Properties of 9984

• 9984 is composite.
• 9984 is not a perfect square.
• Number of divisors: 36.
• Sum of divisors: 28616.

Common Divisors with Another Number?

Looking for the divisors that 9984 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 9984

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √9984 ≈ 99.92. If i divides 9984, then both i and 9984/i are divisors.

1. 1 divides 9984 (9984 ÷ 1 = 9984) → pair (1, 9984)
2. 2 divides 9984 (9984 ÷ 2 = 4992) → pair (2, 4992)
3. 3 divides 9984 (9984 ÷ 3 = 3328) → pair (3, 3328)
4. 4 divides 9984 (9984 ÷ 4 = 2496) → pair (4, 2496)
5. 6 divides 9984 (9984 ÷ 6 = 1664) → pair (6, 1664)
6. 8 divides 9984 (9984 ÷ 8 = 1248) → pair (8, 1248)
7. 12 divides 9984 (9984 ÷ 12 = 832) → pair (12, 832)
8. 13 divides 9984 (9984 ÷ 13 = 768) → pair (13, 768)
9. 16 divides 9984 (9984 ÷ 16 = 624) → pair (16, 624)
10. 24 divides 9984 (9984 ÷ 24 = 416) → pair (24, 416)
11. 26 divides 9984 (9984 ÷ 26 = 384) → pair (26, 384)
12. 32 divides 9984 (9984 ÷ 32 = 312) → pair (32, 312)
13. 39 divides 9984 (9984 ÷ 39 = 256) → pair (39, 256)
14. 48 divides 9984 (9984 ÷ 48 = 208) → pair (48, 208)
15. 52 divides 9984 (9984 ÷ 52 = 192) → pair (52, 192)
16. 64 divides 9984 (9984 ÷ 64 = 156) → pair (64, 156)
17. 78 divides 9984 (9984 ÷ 78 = 128) → pair (78, 128)
18. 96 divides 9984 (9984 ÷ 96 = 104) → pair (96, 104)
19. Collect all unique values: {1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 624, 768, 832, 1248, 1664, 2496, 3328, 4992, 9984} — total 36 divisors.
20. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 16 + 24 + 26 + 32 + 39 + 48 + 52 + 64 + 78 + 96 + 104 + 128 + 156 + 192 + 208 + 256 + 312 + 384 + 416 + 624 + 768 + 832 + 1248 + 1664 + 2496 + 3328 + 4992 + 9984 = 28616.

Nearby Examples

Related Operations for 9984

• Multiples of 9984 — "outward" complement; M is a multiple of 9984 ⇔ 9984 is a divisor of M
• 9984 Prime Factorization — decompose into prime building blocks
• Find GCF of 9984 and another number
• Find LCM of 9984 and another number
• Is 9984 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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