Divisors of 37152: 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 37152

The number 37152 has 48 divisors:

1,  2,  3,  4,  6,  8,  9,  12,  16,  18,  24,  27,  32,  36,  43,  48,  54,  72,  86,  96,  108,  129,  144,  172,  216,  258,  288,  344,  387,  432,  516,  688,  774,  864,  1032,  1161,  1376,  1548,  2064,  2322,  3096,  4128,  4644,  6192,  9288,  12384,  18576,  37152

Divisor Pairs of 37152

Each pair multiplies to 37152:

Number of Divisors

The number 37152 has 48 divisors, written as τ(37152) = 48 in number theory.

Sum of Divisors

σ(37152) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 43 + 48 + 54 + 72 + 86 + 96 + 108 + 129 + 144 + 172 + 216 + 258 + 288 + 344 + 387 + 432 + 516 + 688 + 774 + 864 + 1032 + 1161 + 1376 + 1548 + 2064 + 2322 + 3096 + 4128 + 4644 + 6192 + 9288 + 12384 + 18576 + 37152 = 110880

Prime Factorization of 37152

See the full prime factorization calculator →

Properties of 37152

• 37152 is composite.
• 37152 is not a perfect square.
• Number of divisors: 48.
• Sum of divisors: 110880.

Common Divisors with Another Number?

Looking for the divisors that 37152 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 37152

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √37152 ≈ 192.75. If i divides 37152, then both i and 37152/i are divisors.

1. 1 divides 37152 (37152 ÷ 1 = 37152) → pair (1, 37152)
2. 2 divides 37152 (37152 ÷ 2 = 18576) → pair (2, 18576)
3. 3 divides 37152 (37152 ÷ 3 = 12384) → pair (3, 12384)
4. 4 divides 37152 (37152 ÷ 4 = 9288) → pair (4, 9288)
5. 6 divides 37152 (37152 ÷ 6 = 6192) → pair (6, 6192)
6. 8 divides 37152 (37152 ÷ 8 = 4644) → pair (8, 4644)
7. 9 divides 37152 (37152 ÷ 9 = 4128) → pair (9, 4128)
8. 12 divides 37152 (37152 ÷ 12 = 3096) → pair (12, 3096)
9. 16 divides 37152 (37152 ÷ 16 = 2322) → pair (16, 2322)
10. 18 divides 37152 (37152 ÷ 18 = 2064) → pair (18, 2064)
11. 24 divides 37152 (37152 ÷ 24 = 1548) → pair (24, 1548)
12. 27 divides 37152 (37152 ÷ 27 = 1376) → pair (27, 1376)
13. 32 divides 37152 (37152 ÷ 32 = 1161) → pair (32, 1161)
14. 36 divides 37152 (37152 ÷ 36 = 1032) → pair (36, 1032)
15. 43 divides 37152 (37152 ÷ 43 = 864) → pair (43, 864)
16. 48 divides 37152 (37152 ÷ 48 = 774) → pair (48, 774)
17. 54 divides 37152 (37152 ÷ 54 = 688) → pair (54, 688)
18. 72 divides 37152 (37152 ÷ 72 = 516) → pair (72, 516)
19. 86 divides 37152 (37152 ÷ 86 = 432) → pair (86, 432)
20. 96 divides 37152 (37152 ÷ 96 = 387) → pair (96, 387)
21. 108 divides 37152 (37152 ÷ 108 = 344) → pair (108, 344)
22. 129 divides 37152 (37152 ÷ 129 = 288) → pair (129, 288)
23. 144 divides 37152 (37152 ÷ 144 = 258) → pair (144, 258)
24. 172 divides 37152 (37152 ÷ 172 = 216) → pair (172, 216)
25. Collect all unique values: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 43, 48, 54, 72, 86, 96, 108, 129, 144, 172, 216, 258, 288, 344, 387, 432, 516, 688, 774, 864, 1032, 1161, 1376, 1548, 2064, 2322, 3096, 4128, 4644, 6192, 9288, 12384, 18576, 37152} — total 48 divisors.
26. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 43 + 48 + 54 + 72 + 86 + 96 + 108 + 129 + 144 + 172 + 216 + 258 + 288 + 344 + 387 + 432 + 516 + 688 + 774 + 864 + 1032 + 1161 + 1376 + 1548 + 2064 + 2322 + 3096 + 4128 + 4644 + 6192 + 9288 + 12384 + 18576 + 37152 = 110880.

Nearby Examples

Related Operations for 37152

• Multiples of a Number — "outward" complement of divisors
• 37152 Prime Factorization — decompose into prime building blocks
• Find GCF of 37152 and another number
• Find LCM of 37152 and another number
• Is 37152 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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