Divisors of 21000: All 64 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 21000

The number 21000 has 64 divisors:

1,  2,  3,  4,  5,  6,  7,  8,  10,  12,  14,  15,  20,  21,  24,  25,  28,  30,  35,  40,  42,  50,  56,  60,  70,  75,  84,  100,  105,  120,  125,  140,  150,  168,  175,  200,  210,  250,  280,  300,  350,  375,  420,  500,  525,  600,  700,  750,  840,  875,  1000,  1050,  1400,  1500,  1750,  2100,  2625,  3000,  3500,  4200,  5250,  7000,  10500,  21000

Divisor Pairs of 21000

Each pair multiplies to 21000:

Number of Divisors

The number 21000 has 64 divisors, written as τ(21000) = 64 in number theory.

Sum of Divisors

σ(21000) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 20 + 21 + 24 + 25 + 28 + 30 + 35 + 40 + 42 + 50 + 56 + 60 + 70 + 75 + 84 + 100 + 105 + 120 + 125 + 140 + 150 + 168 + 175 + 200 + 210 + 250 + 280 + 300 + 350 + 375 + 420 + 500 + 525 + 600 + 700 + 750 + 840 + 875 + 1000 + 1050 + 1400 + 1500 + 1750 + 2100 + 2625 + 3000 + 3500 + 4200 + 5250 + 7000 + 10500 + 21000 = 74880

Prime Factorization of 21000

See the full prime factorization calculator →

Properties of 21000

• 21000 is composite.
• 21000 is not a perfect square.
• Number of divisors: 64.
• Sum of divisors: 74880.

Common Divisors with Another Number?

Looking for the divisors that 21000 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 21000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √21000 ≈ 144.91. If i divides 21000, then both i and 21000/i are divisors.

1. 1 divides 21000 (21000 ÷ 1 = 21000) → pair (1, 21000)
2. 2 divides 21000 (21000 ÷ 2 = 10500) → pair (2, 10500)
3. 3 divides 21000 (21000 ÷ 3 = 7000) → pair (3, 7000)
4. 4 divides 21000 (21000 ÷ 4 = 5250) → pair (4, 5250)
5. 5 divides 21000 (21000 ÷ 5 = 4200) → pair (5, 4200)
6. 6 divides 21000 (21000 ÷ 6 = 3500) → pair (6, 3500)
7. 7 divides 21000 (21000 ÷ 7 = 3000) → pair (7, 3000)
8. 8 divides 21000 (21000 ÷ 8 = 2625) → pair (8, 2625)
9. 10 divides 21000 (21000 ÷ 10 = 2100) → pair (10, 2100)
10. 12 divides 21000 (21000 ÷ 12 = 1750) → pair (12, 1750)
11. 14 divides 21000 (21000 ÷ 14 = 1500) → pair (14, 1500)
12. 15 divides 21000 (21000 ÷ 15 = 1400) → pair (15, 1400)
13. 20 divides 21000 (21000 ÷ 20 = 1050) → pair (20, 1050)
14. 21 divides 21000 (21000 ÷ 21 = 1000) → pair (21, 1000)
15. 24 divides 21000 (21000 ÷ 24 = 875) → pair (24, 875)
16. 25 divides 21000 (21000 ÷ 25 = 840) → pair (25, 840)
17. 28 divides 21000 (21000 ÷ 28 = 750) → pair (28, 750)
18. 30 divides 21000 (21000 ÷ 30 = 700) → pair (30, 700)
19. 35 divides 21000 (21000 ÷ 35 = 600) → pair (35, 600)
20. 40 divides 21000 (21000 ÷ 40 = 525) → pair (40, 525)
21. 42 divides 21000 (21000 ÷ 42 = 500) → pair (42, 500)
22. 50 divides 21000 (21000 ÷ 50 = 420) → pair (50, 420)
23. 56 divides 21000 (21000 ÷ 56 = 375) → pair (56, 375)
24. 60 divides 21000 (21000 ÷ 60 = 350) → pair (60, 350)
25. 70 divides 21000 (21000 ÷ 70 = 300) → pair (70, 300)
26. 75 divides 21000 (21000 ÷ 75 = 280) → pair (75, 280)
27. 84 divides 21000 (21000 ÷ 84 = 250) → pair (84, 250)
28. 100 divides 21000 (21000 ÷ 100 = 210) → pair (100, 210)
29. 105 divides 21000 (21000 ÷ 105 = 200) → pair (105, 200)
30. 120 divides 21000 (21000 ÷ 120 = 175) → pair (120, 175)
31. 125 divides 21000 (21000 ÷ 125 = 168) → pair (125, 168)
32. 140 divides 21000 (21000 ÷ 140 = 150) → pair (140, 150)
33. Collect all unique values: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 125, 140, 150, 168, 175, 200, 210, 250, 280, 300, 350, 375, 420, 500, 525, 600, 700, 750, 840, 875, 1000, 1050, 1400, 1500, 1750, 2100, 2625, 3000, 3500, 4200, 5250, 7000, 10500, 21000} — total 64 divisors.
34. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 20 + 21 + 24 + 25 + 28 + 30 + 35 + 40 + 42 + 50 + 56 + 60 + 70 + 75 + 84 + 100 + 105 + 120 + 125 + 140 + 150 + 168 + 175 + 200 + 210 + 250 + 280 + 300 + 350 + 375 + 420 + 500 + 525 + 600 + 700 + 750 + 840 + 875 + 1000 + 1050 + 1400 + 1500 + 1750 + 2100 + 2625 + 3000 + 3500 + 4200 + 5250 + 7000 + 10500 + 21000 = 74880.

Nearby Examples

Related Operations for 21000

• Multiples of a Number — "outward" complement of divisors
• 21000 Prime Factorization — decompose into prime building blocks
• Find GCF of 21000 and another number
• Find LCM of 21000 and another number
• Is 21000 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

Find all divisors of these numbers: