Divisors of 42210: 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 42210

The number 42210 has 48 divisors:

1,  2,  3,  5,  6,  7,  9,  10,  14,  15,  18,  21,  30,  35,  42,  45,  63,  67,  70,  90,  105,  126,  134,  201,  210,  315,  335,  402,  469,  603,  630,  670,  938,  1005,  1206,  1407,  2010,  2345,  2814,  3015,  4221,  4690,  6030,  7035,  8442,  14070,  21105,  42210

Divisor Pairs of 42210

Each pair multiplies to 42210:

Number of Divisors

The number 42210 has 48 divisors, written as τ(42210) = 48 in number theory.

Sum of Divisors

σ(42210) = 1 + 2 + 3 + 5 + 6 + 7 + 9 + 10 + 14 + 15 + 18 + 21 + 30 + 35 + 42 + 45 + 63 + 67 + 70 + 90 + 105 + 126 + 134 + 201 + 210 + 315 + 335 + 402 + 469 + 603 + 630 + 670 + 938 + 1005 + 1206 + 1407 + 2010 + 2345 + 2814 + 3015 + 4221 + 4690 + 6030 + 7035 + 8442 + 14070 + 21105 + 42210 = 127296

Prime Factorization of 42210

See the full prime factorization calculator →

Properties of 42210

• 42210 is composite.
• 42210 is not a perfect square.
• Number of divisors: 48.
• Sum of divisors: 127296.

Common Divisors with Another Number?

Looking for the divisors that 42210 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 42210

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √42210 ≈ 205.45. If i divides 42210, then both i and 42210/i are divisors.

1. 1 divides 42210 (42210 ÷ 1 = 42210) → pair (1, 42210)
2. 2 divides 42210 (42210 ÷ 2 = 21105) → pair (2, 21105)
3. 3 divides 42210 (42210 ÷ 3 = 14070) → pair (3, 14070)
4. 5 divides 42210 (42210 ÷ 5 = 8442) → pair (5, 8442)
5. 6 divides 42210 (42210 ÷ 6 = 7035) → pair (6, 7035)
6. 7 divides 42210 (42210 ÷ 7 = 6030) → pair (7, 6030)
7. 9 divides 42210 (42210 ÷ 9 = 4690) → pair (9, 4690)
8. 10 divides 42210 (42210 ÷ 10 = 4221) → pair (10, 4221)
9. 14 divides 42210 (42210 ÷ 14 = 3015) → pair (14, 3015)
10. 15 divides 42210 (42210 ÷ 15 = 2814) → pair (15, 2814)
11. 18 divides 42210 (42210 ÷ 18 = 2345) → pair (18, 2345)
12. 21 divides 42210 (42210 ÷ 21 = 2010) → pair (21, 2010)
13. 30 divides 42210 (42210 ÷ 30 = 1407) → pair (30, 1407)
14. 35 divides 42210 (42210 ÷ 35 = 1206) → pair (35, 1206)
15. 42 divides 42210 (42210 ÷ 42 = 1005) → pair (42, 1005)
16. 45 divides 42210 (42210 ÷ 45 = 938) → pair (45, 938)
17. 63 divides 42210 (42210 ÷ 63 = 670) → pair (63, 670)
18. 67 divides 42210 (42210 ÷ 67 = 630) → pair (67, 630)
19. 70 divides 42210 (42210 ÷ 70 = 603) → pair (70, 603)
20. 90 divides 42210 (42210 ÷ 90 = 469) → pair (90, 469)
21. 105 divides 42210 (42210 ÷ 105 = 402) → pair (105, 402)
22. 126 divides 42210 (42210 ÷ 126 = 335) → pair (126, 335)
23. 134 divides 42210 (42210 ÷ 134 = 315) → pair (134, 315)
24. 201 divides 42210 (42210 ÷ 201 = 210) → pair (201, 210)
25. Collect all unique values: {1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 67, 70, 90, 105, 126, 134, 201, 210, 315, 335, 402, 469, 603, 630, 670, 938, 1005, 1206, 1407, 2010, 2345, 2814, 3015, 4221, 4690, 6030, 7035, 8442, 14070, 21105, 42210} — total 48 divisors.
26. Sum: 1 + 2 + 3 + 5 + 6 + 7 + 9 + 10 + 14 + 15 + 18 + 21 + 30 + 35 + 42 + 45 + 63 + 67 + 70 + 90 + 105 + 126 + 134 + 201 + 210 + 315 + 335 + 402 + 469 + 603 + 630 + 670 + 938 + 1005 + 1206 + 1407 + 2010 + 2345 + 2814 + 3015 + 4221 + 4690 + 6030 + 7035 + 8442 + 14070 + 21105 + 42210 = 127296.

Nearby Examples

Related Operations for 42210

• Multiples of a Number — "outward" complement of divisors
• 42210 Prime Factorization — decompose into prime building blocks
• Find GCF of 42210 and another number
• Find LCM of 42210 and another number
• Is 42210 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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