Divisors of 35040: 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 35040

The number 35040 has 48 divisors:

1,  2,  3,  4,  5,  6,  8,  10,  12,  15,  16,  20,  24,  30,  32,  40,  48,  60,  73,  80,  96,  120,  146,  160,  219,  240,  292,  365,  438,  480,  584,  730,  876,  1095,  1168,  1460,  1752,  2190,  2336,  2920,  3504,  4380,  5840,  7008,  8760,  11680,  17520,  35040

Divisor Pairs of 35040

Each pair multiplies to 35040:

Number of Divisors

The number 35040 has 48 divisors, written as τ(35040) = 48 in number theory.

Sum of Divisors

σ(35040) = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 73 + 80 + 96 + 120 + 146 + 160 + 219 + 240 + 292 + 365 + 438 + 480 + 584 + 730 + 876 + 1095 + 1168 + 1460 + 1752 + 2190 + 2336 + 2920 + 3504 + 4380 + 5840 + 7008 + 8760 + 11680 + 17520 + 35040 = 111888

Prime Factorization of 35040

See the full prime factorization calculator →

Properties of 35040

• 35040 is composite.
• 35040 is not a perfect square.
• Number of divisors: 48.
• Sum of divisors: 111888.

Common Divisors with Another Number?

Looking for the divisors that 35040 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 35040

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √35040 ≈ 187.19. If i divides 35040, then both i and 35040/i are divisors.

1. 1 divides 35040 (35040 ÷ 1 = 35040) → pair (1, 35040)
2. 2 divides 35040 (35040 ÷ 2 = 17520) → pair (2, 17520)
3. 3 divides 35040 (35040 ÷ 3 = 11680) → pair (3, 11680)
4. 4 divides 35040 (35040 ÷ 4 = 8760) → pair (4, 8760)
5. 5 divides 35040 (35040 ÷ 5 = 7008) → pair (5, 7008)
6. 6 divides 35040 (35040 ÷ 6 = 5840) → pair (6, 5840)
7. 8 divides 35040 (35040 ÷ 8 = 4380) → pair (8, 4380)
8. 10 divides 35040 (35040 ÷ 10 = 3504) → pair (10, 3504)
9. 12 divides 35040 (35040 ÷ 12 = 2920) → pair (12, 2920)
10. 15 divides 35040 (35040 ÷ 15 = 2336) → pair (15, 2336)
11. 16 divides 35040 (35040 ÷ 16 = 2190) → pair (16, 2190)
12. 20 divides 35040 (35040 ÷ 20 = 1752) → pair (20, 1752)
13. 24 divides 35040 (35040 ÷ 24 = 1460) → pair (24, 1460)
14. 30 divides 35040 (35040 ÷ 30 = 1168) → pair (30, 1168)
15. 32 divides 35040 (35040 ÷ 32 = 1095) → pair (32, 1095)
16. 40 divides 35040 (35040 ÷ 40 = 876) → pair (40, 876)
17. 48 divides 35040 (35040 ÷ 48 = 730) → pair (48, 730)
18. 60 divides 35040 (35040 ÷ 60 = 584) → pair (60, 584)
19. 73 divides 35040 (35040 ÷ 73 = 480) → pair (73, 480)
20. 80 divides 35040 (35040 ÷ 80 = 438) → pair (80, 438)
21. 96 divides 35040 (35040 ÷ 96 = 365) → pair (96, 365)
22. 120 divides 35040 (35040 ÷ 120 = 292) → pair (120, 292)
23. 146 divides 35040 (35040 ÷ 146 = 240) → pair (146, 240)
24. 160 divides 35040 (35040 ÷ 160 = 219) → pair (160, 219)
25. Collect all unique values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 73, 80, 96, 120, 146, 160, 219, 240, 292, 365, 438, 480, 584, 730, 876, 1095, 1168, 1460, 1752, 2190, 2336, 2920, 3504, 4380, 5840, 7008, 8760, 11680, 17520, 35040} — total 48 divisors.
26. Sum: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 73 + 80 + 96 + 120 + 146 + 160 + 219 + 240 + 292 + 365 + 438 + 480 + 584 + 730 + 876 + 1095 + 1168 + 1460 + 1752 + 2190 + 2336 + 2920 + 3504 + 4380 + 5840 + 7008 + 8760 + 11680 + 17520 + 35040 = 111888.

Nearby Examples

Related Operations for 35040

• Multiples of a Number — "outward" complement of divisors
• 35040 Prime Factorization — decompose into prime building blocks
• Find GCF of 35040 and another number
• Find LCM of 35040 and another number
• Is 35040 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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