Divisors of 32448: All 42 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 32448

The number 32448 has 42 divisors:

1,  2,  3,  4,  6,  8,  12,  13,  16,  24,  26,  32,  39,  48,  52,  64,  78,  96,  104,  156,  169,  192,  208,  312,  338,  416,  507,  624,  676,  832,  1014,  1248,  1352,  2028,  2496,  2704,  4056,  5408,  8112,  10816,  16224,  32448

Divisor Pairs of 32448

Each pair multiplies to 32448:

Number of Divisors

The number 32448 has 42 divisors, written as τ(32448) = 42 in number theory.

Sum of Divisors

σ(32448) = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 16 + 24 + 26 + 32 + 39 + 48 + 52 + 64 + 78 + 96 + 104 + 156 + 169 + 192 + 208 + 312 + 338 + 416 + 507 + 624 + 676 + 832 + 1014 + 1248 + 1352 + 2028 + 2496 + 2704 + 4056 + 5408 + 8112 + 10816 + 16224 + 32448 = 92964

Prime Factorization of 32448

See the full prime factorization calculator →

Properties of 32448

• 32448 is composite.
• 32448 is not a perfect square.
• Number of divisors: 42.
• Sum of divisors: 92964.

Common Divisors with Another Number?

Looking for the divisors that 32448 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 32448

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √32448 ≈ 180.13. If i divides 32448, then both i and 32448/i are divisors.

1. 1 divides 32448 (32448 ÷ 1 = 32448) → pair (1, 32448)
2. 2 divides 32448 (32448 ÷ 2 = 16224) → pair (2, 16224)
3. 3 divides 32448 (32448 ÷ 3 = 10816) → pair (3, 10816)
4. 4 divides 32448 (32448 ÷ 4 = 8112) → pair (4, 8112)
5. 6 divides 32448 (32448 ÷ 6 = 5408) → pair (6, 5408)
6. 8 divides 32448 (32448 ÷ 8 = 4056) → pair (8, 4056)
7. 12 divides 32448 (32448 ÷ 12 = 2704) → pair (12, 2704)
8. 13 divides 32448 (32448 ÷ 13 = 2496) → pair (13, 2496)
9. 16 divides 32448 (32448 ÷ 16 = 2028) → pair (16, 2028)
10. 24 divides 32448 (32448 ÷ 24 = 1352) → pair (24, 1352)
11. 26 divides 32448 (32448 ÷ 26 = 1248) → pair (26, 1248)
12. 32 divides 32448 (32448 ÷ 32 = 1014) → pair (32, 1014)
13. 39 divides 32448 (32448 ÷ 39 = 832) → pair (39, 832)
14. 48 divides 32448 (32448 ÷ 48 = 676) → pair (48, 676)
15. 52 divides 32448 (32448 ÷ 52 = 624) → pair (52, 624)
16. 64 divides 32448 (32448 ÷ 64 = 507) → pair (64, 507)
17. 78 divides 32448 (32448 ÷ 78 = 416) → pair (78, 416)
18. 96 divides 32448 (32448 ÷ 96 = 338) → pair (96, 338)
19. 104 divides 32448 (32448 ÷ 104 = 312) → pair (104, 312)
20. 156 divides 32448 (32448 ÷ 156 = 208) → pair (156, 208)
21. 169 divides 32448 (32448 ÷ 169 = 192) → pair (169, 192)
22. Collect all unique values: {1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 156, 169, 192, 208, 312, 338, 416, 507, 624, 676, 832, 1014, 1248, 1352, 2028, 2496, 2704, 4056, 5408, 8112, 10816, 16224, 32448} — total 42 divisors.
23. Sum: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 16 + 24 + 26 + 32 + 39 + 48 + 52 + 64 + 78 + 96 + 104 + 156 + 169 + 192 + 208 + 312 + 338 + 416 + 507 + 624 + 676 + 832 + 1014 + 1248 + 1352 + 2028 + 2496 + 2704 + 4056 + 5408 + 8112 + 10816 + 16224 + 32448 = 92964.

Nearby Examples

Related Operations for 32448

• Multiples of a Number — "outward" complement of divisors
• 32448 Prime Factorization — decompose into prime building blocks
• Find GCF of 32448 and another number
• Find LCM of 32448 and another number
• Is 32448 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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