Divisors of 42768: All 60 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 42768

The number 42768 has 60 divisors:

1,  2,  3,  4,  6,  8,  9,  11,  12,  16,  18,  22,  24,  27,  33,  36,  44,  48,  54,  66,  72,  81,  88,  99,  108,  132,  144,  162,  176,  198,  216,  243,  264,  297,  324,  396,  432,  486,  528,  594,  648,  792,  891,  972,  1188,  1296,  1584,  1782,  1944,  2376,  2673,  3564,  3888,  4752,  5346,  7128,  10692,  14256,  21384,  42768

Divisor Pairs of 42768

Each pair multiplies to 42768:

Number of Divisors

The number 42768 has 60 divisors, written as τ(42768) = 60 in number theory.

Sum of Divisors

σ(42768) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 11 + 12 + 16 + 18 + 22 + 24 + 27 + 33 + 36 + 44 + 48 + 54 + 66 + 72 + 81 + 88 + 99 + 108 + 132 + 144 + 162 + 176 + 198 + 216 + 243 + 264 + 297 + 324 + 396 + 432 + 486 + 528 + 594 + 648 + 792 + 891 + 972 + 1188 + 1296 + 1584 + 1782 + 1944 + 2376 + 2673 + 3564 + 3888 + 4752 + 5346 + 7128 + 10692 + 14256 + 21384 + 42768 = 135408

Prime Factorization of 42768

See the full prime factorization calculator →

Properties of 42768

• 42768 is composite.
• 42768 is not a perfect square.
• Number of divisors: 60.
• Sum of divisors: 135408.

Common Divisors with Another Number?

Looking for the divisors that 42768 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 42768

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √42768 ≈ 206.80. If i divides 42768, then both i and 42768/i are divisors.

1. 1 divides 42768 (42768 ÷ 1 = 42768) → pair (1, 42768)
2. 2 divides 42768 (42768 ÷ 2 = 21384) → pair (2, 21384)
3. 3 divides 42768 (42768 ÷ 3 = 14256) → pair (3, 14256)
4. 4 divides 42768 (42768 ÷ 4 = 10692) → pair (4, 10692)
5. 6 divides 42768 (42768 ÷ 6 = 7128) → pair (6, 7128)
6. 8 divides 42768 (42768 ÷ 8 = 5346) → pair (8, 5346)
7. 9 divides 42768 (42768 ÷ 9 = 4752) → pair (9, 4752)
8. 11 divides 42768 (42768 ÷ 11 = 3888) → pair (11, 3888)
9. 12 divides 42768 (42768 ÷ 12 = 3564) → pair (12, 3564)
10. 16 divides 42768 (42768 ÷ 16 = 2673) → pair (16, 2673)
11. 18 divides 42768 (42768 ÷ 18 = 2376) → pair (18, 2376)
12. 22 divides 42768 (42768 ÷ 22 = 1944) → pair (22, 1944)
13. 24 divides 42768 (42768 ÷ 24 = 1782) → pair (24, 1782)
14. 27 divides 42768 (42768 ÷ 27 = 1584) → pair (27, 1584)
15. 33 divides 42768 (42768 ÷ 33 = 1296) → pair (33, 1296)
16. 36 divides 42768 (42768 ÷ 36 = 1188) → pair (36, 1188)
17. 44 divides 42768 (42768 ÷ 44 = 972) → pair (44, 972)
18. 48 divides 42768 (42768 ÷ 48 = 891) → pair (48, 891)
19. 54 divides 42768 (42768 ÷ 54 = 792) → pair (54, 792)
20. 66 divides 42768 (42768 ÷ 66 = 648) → pair (66, 648)
21. 72 divides 42768 (42768 ÷ 72 = 594) → pair (72, 594)
22. 81 divides 42768 (42768 ÷ 81 = 528) → pair (81, 528)
23. 88 divides 42768 (42768 ÷ 88 = 486) → pair (88, 486)
24. 99 divides 42768 (42768 ÷ 99 = 432) → pair (99, 432)
25. 108 divides 42768 (42768 ÷ 108 = 396) → pair (108, 396)
26. 132 divides 42768 (42768 ÷ 132 = 324) → pair (132, 324)
27. 144 divides 42768 (42768 ÷ 144 = 297) → pair (144, 297)
28. 162 divides 42768 (42768 ÷ 162 = 264) → pair (162, 264)
29. 176 divides 42768 (42768 ÷ 176 = 243) → pair (176, 243)
30. 198 divides 42768 (42768 ÷ 198 = 216) → pair (198, 216)
31. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 33, 36, 44, 48, 54, 66, 72, 81, 88, 99, 108, 132, 144, 162, 176, 198, 216, 243, 264, 297, 324, 396, 432, 486, 528, 594, 648, 792, 891, 972, 1188, 1296, 1584, 1782, 1944, 2376, 2673, 3564, 3888, 4752, 5346, 7128, 10692, 14256, 21384, 42768} — total 60 divisors.
32. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 11 + 12 + 16 + 18 + 22 + 24 + 27 + 33 + 36 + 44 + 48 + 54 + 66 + 72 + 81 + 88 + 99 + 108 + 132 + 144 + 162 + 176 + 198 + 216 + 243 + 264 + 297 + 324 + 396 + 432 + 486 + 528 + 594 + 648 + 792 + 891 + 972 + 1188 + 1296 + 1584 + 1782 + 1944 + 2376 + 2673 + 3564 + 3888 + 4752 + 5346 + 7128 + 10692 + 14256 + 21384 + 42768 = 135408.

Nearby Examples

Related Operations for 42768

• Multiples of a Number — "outward" complement of divisors
• 42768 Prime Factorization — decompose into prime building blocks
• Find GCF of 42768 and another number
• Find LCM of 42768 and another number
• Is 42768 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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