Divisors of 9828: All 48 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 9828

The number 9828 has 48 divisors:

1,  2,  3,  4,  6,  7,  9,  12,  13,  14,  18,  21,  26,  27,  28,  36,  39,  42,  52,  54,  63,  78,  84,  91,  108,  117,  126,  156,  182,  189,  234,  252,  273,  351,  364,  378,  468,  546,  702,  756,  819,  1092,  1404,  1638,  2457,  3276,  4914,  9828

Divisor Pairs of 9828

Each pair multiplies to 9828:

Number of Divisors

The number 9828 has 48 divisors, written as τ(9828) = 48 in number theory.

Sum of Divisors

σ(9828) = 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 13 + 14 + 18 + 21 + 26 + 27 + 28 + 36 + 39 + 42 + 52 + 54 + 63 + 78 + 84 + 91 + 108 + 117 + 126 + 156 + 182 + 189 + 234 + 252 + 273 + 351 + 364 + 378 + 468 + 546 + 702 + 756 + 819 + 1092 + 1404 + 1638 + 2457 + 3276 + 4914 + 9828 = 31360

Prime Factorization of 9828

See the full prime factorization calculator →

Properties of 9828

• 9828 is composite.
• 9828 is not a perfect square.
• Number of divisors: 48.
• Sum of divisors: 31360.

Common Divisors with Another Number?

Looking for the divisors that 9828 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 9828

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √9828 ≈ 99.14. If i divides 9828, then both i and 9828/i are divisors.

1. 1 divides 9828 (9828 ÷ 1 = 9828) → pair (1, 9828)
2. 2 divides 9828 (9828 ÷ 2 = 4914) → pair (2, 4914)
3. 3 divides 9828 (9828 ÷ 3 = 3276) → pair (3, 3276)
4. 4 divides 9828 (9828 ÷ 4 = 2457) → pair (4, 2457)
5. 6 divides 9828 (9828 ÷ 6 = 1638) → pair (6, 1638)
6. 7 divides 9828 (9828 ÷ 7 = 1404) → pair (7, 1404)
7. 9 divides 9828 (9828 ÷ 9 = 1092) → pair (9, 1092)
8. 12 divides 9828 (9828 ÷ 12 = 819) → pair (12, 819)
9. 13 divides 9828 (9828 ÷ 13 = 756) → pair (13, 756)
10. 14 divides 9828 (9828 ÷ 14 = 702) → pair (14, 702)
11. 18 divides 9828 (9828 ÷ 18 = 546) → pair (18, 546)
12. 21 divides 9828 (9828 ÷ 21 = 468) → pair (21, 468)
13. 26 divides 9828 (9828 ÷ 26 = 378) → pair (26, 378)
14. 27 divides 9828 (9828 ÷ 27 = 364) → pair (27, 364)
15. 28 divides 9828 (9828 ÷ 28 = 351) → pair (28, 351)
16. 36 divides 9828 (9828 ÷ 36 = 273) → pair (36, 273)
17. 39 divides 9828 (9828 ÷ 39 = 252) → pair (39, 252)
18. 42 divides 9828 (9828 ÷ 42 = 234) → pair (42, 234)
19. 52 divides 9828 (9828 ÷ 52 = 189) → pair (52, 189)
20. 54 divides 9828 (9828 ÷ 54 = 182) → pair (54, 182)
21. 63 divides 9828 (9828 ÷ 63 = 156) → pair (63, 156)
22. 78 divides 9828 (9828 ÷ 78 = 126) → pair (78, 126)
23. 84 divides 9828 (9828 ÷ 84 = 117) → pair (84, 117)
24. 91 divides 9828 (9828 ÷ 91 = 108) → pair (91, 108)
25. Collect all unique values: {1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 18, 21, 26, 27, 28, 36, 39, 42, 52, 54, 63, 78, 84, 91, 108, 117, 126, 156, 182, 189, 234, 252, 273, 351, 364, 378, 468, 546, 702, 756, 819, 1092, 1404, 1638, 2457, 3276, 4914, 9828} — total 48 divisors.
26. Sum: 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 13 + 14 + 18 + 21 + 26 + 27 + 28 + 36 + 39 + 42 + 52 + 54 + 63 + 78 + 84 + 91 + 108 + 117 + 126 + 156 + 182 + 189 + 234 + 252 + 273 + 351 + 364 + 378 + 468 + 546 + 702 + 756 + 819 + 1092 + 1404 + 1638 + 2457 + 3276 + 4914 + 9828 = 31360.

Nearby Examples

Related Operations for 9828

• Multiples of 9828 — "outward" complement; M is a multiple of 9828 ⇔ 9828 is a divisor of M
• 9828 Prime Factorization — decompose into prime building blocks
• Find GCF of 9828 and another number
• Find LCM of 9828 and another number
• Is 9828 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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