Divisors of 21960: All 48 Factors

Quick Answer

21960 has 48 divisors (factors): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 61, 72, 90, 120, 122, 180, 183, 244, 305, 360, 366, 488, 549, 610, 732, 915, 1098, 1220, 1464, 1830, 2196, 2440, 2745, 3660, 4392, 5490, 7320, 10980, 21960.

Sum: 72540.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

  Ex.: 12, 36, 100, 1024, 1728, etc.
48 divisors
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 61, 72, 90, 120, 122, 180, 183, 244, 305, 360, 366, 488, 549, 610, 732, 915, 1098, 1220, 1464, 1830, 2196, 2440, 2745, 3660, 4392, 5490, 7320, 10980, 21960

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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 21960

The number 21960 has 48 divisors:

1,  2,  3,  4,  5,  6,  8,  9,  10,  12,  15,  18,  20,  24,  30,  36,  40,  45,  60,  61,  72,  90,  120,  122,  180,  183,  244,  305,  360,  366,  488,  549,  610,  732,  915,  1098,  1220,  1464,  1830,  2196,  2440,  2745,  3660,  4392,  5490,  7320,  10980,  21960

Divisor Pairs of 21960

Each pair multiplies to 21960:

Factor 1×Factor 2=Product
1×21960=21960
2×10980=21960
3×7320=21960
4×5490=21960
5×4392=21960
6×3660=21960
8×2745=21960
9×2440=21960
10×2196=21960
12×1830=21960
15×1464=21960
18×1220=21960
20×1098=21960
24×915=21960
30×732=21960
36×610=21960
40×549=21960
45×488=21960
60×366=21960
61×360=21960
72×305=21960
90×244=21960
120×183=21960
122×180=21960

Number of Divisors

The number 21960 has 48 divisors, written as τ(21960) = 48 in number theory.

Sum of Divisors

σ(21960) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 60 + 61 + 72 + 90 + 120 + 122 + 180 + 183 + 244 + 305 + 360 + 366 + 488 + 549 + 610 + 732 + 915 + 1098 + 1220 + 1464 + 1830 + 2196 + 2440 + 2745 + 3660 + 4392 + 5490 + 7320 + 10980 + 21960 = 72540

Prime Factorization of 21960

See the full prime factorization calculator →

Properties of 21960

  • 21960 is composite.
  • 21960 is not a perfect square.
  • Number of divisors: 48.
  • Sum of divisors: 72540.

Common Divisors with Another Number?

Looking for the divisors that 21960 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 21960

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √21960 ≈ 148.19. If i divides 21960, then both i and 21960/i are divisors.

  1. 1 divides 21960 (21960 ÷ 1 = 21960) → pair (1, 21960)
  2. 2 divides 21960 (21960 ÷ 2 = 10980) → pair (2, 10980)
  3. 3 divides 21960 (21960 ÷ 3 = 7320) → pair (3, 7320)
  4. 4 divides 21960 (21960 ÷ 4 = 5490) → pair (4, 5490)
  5. 5 divides 21960 (21960 ÷ 5 = 4392) → pair (5, 4392)
  6. 6 divides 21960 (21960 ÷ 6 = 3660) → pair (6, 3660)
  7. 8 divides 21960 (21960 ÷ 8 = 2745) → pair (8, 2745)
  8. 9 divides 21960 (21960 ÷ 9 = 2440) → pair (9, 2440)
  9. 10 divides 21960 (21960 ÷ 10 = 2196) → pair (10, 2196)
  10. 12 divides 21960 (21960 ÷ 12 = 1830) → pair (12, 1830)
  11. 15 divides 21960 (21960 ÷ 15 = 1464) → pair (15, 1464)
  12. 18 divides 21960 (21960 ÷ 18 = 1220) → pair (18, 1220)
  13. 20 divides 21960 (21960 ÷ 20 = 1098) → pair (20, 1098)
  14. 24 divides 21960 (21960 ÷ 24 = 915) → pair (24, 915)
  15. 30 divides 21960 (21960 ÷ 30 = 732) → pair (30, 732)
  16. 36 divides 21960 (21960 ÷ 36 = 610) → pair (36, 610)
  17. 40 divides 21960 (21960 ÷ 40 = 549) → pair (40, 549)
  18. 45 divides 21960 (21960 ÷ 45 = 488) → pair (45, 488)
  19. 60 divides 21960 (21960 ÷ 60 = 366) → pair (60, 366)
  20. 61 divides 21960 (21960 ÷ 61 = 360) → pair (61, 360)
  21. 72 divides 21960 (21960 ÷ 72 = 305) → pair (72, 305)
  22. 90 divides 21960 (21960 ÷ 90 = 244) → pair (90, 244)
  23. 120 divides 21960 (21960 ÷ 120 = 183) → pair (120, 183)
  24. 122 divides 21960 (21960 ÷ 122 = 180) → pair (122, 180)
  25. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 61, 72, 90, 120, 122, 180, 183, 244, 305, 360, 366, 488, 549, 610, 732, 915, 1098, 1220, 1464, 1830, 2196, 2440, 2745, 3660, 4392, 5490, 7320, 10980, 21960} — total 48 divisors.
  26. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 60 + 61 + 72 + 90 + 120 + 122 + 180 + 183 + 244 + 305 + 360 + 366 + 488 + 549 + 610 + 732 + 915 + 1098 + 1220 + 1464 + 1830 + 2196 + 2440 + 2745 + 3660 + 4392 + 5490 + 7320 + 10980 + 21960 = 72540.

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Related Operations for 21960

See also our tables of divisors:

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

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