Divisors of 48400: All 45 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 48400

The number 48400 has 45 divisors:

1,  2,  4,  5,  8,  10,  11,  16,  20,  22,  25,  40,  44,  50,  55,  80,  88,  100,  110,  121,  176,  200,  220,  242,  275,  400,  440,  484,  550,  605,  880,  968,  1100,  1210,  1936,  2200,  2420,  3025,  4400,  4840,  6050,  9680,  12100,  24200,  48400

Divisor Pairs of 48400

Each pair multiplies to 48400:

Note: the last pair has identical factors (220 × 220) because 48400 is a perfect square.

Number of Divisors

The number 48400 has 45 divisors, written as τ(48400) = 45 in number theory.

⚡ Notice: 48400 has an odd number of divisors — this means 48400 is a perfect square (√48400 = 220).

Sum of Divisors

σ(48400) = 1 + 2 + 4 + 5 + 8 + 10 + 11 + 16 + 20 + 22 + 25 + 40 + 44 + 50 + 55 + 80 + 88 + 100 + 110 + 121 + 176 + 200 + 220 + 242 + 275 + 400 + 440 + 484 + 550 + 605 + 880 + 968 + 1100 + 1210 + 1936 + 2200 + 2420 + 3025 + 4400 + 4840 + 6050 + 9680 + 12100 + 24200 + 48400 = 127813

Prime Factorization of 48400

See the full prime factorization calculator →

Properties of 48400

• 48400 is composite.
• 48400 is a perfect square (√48400 = 220).
• Number of divisors: 45.
• Sum of divisors: 127813.

Common Divisors with Another Number?

Looking for the divisors that 48400 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 48400

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √48400 ≈ 220.00. If i divides 48400, then both i and 48400/i are divisors.

1. 1 divides 48400 (48400 ÷ 1 = 48400) → pair (1, 48400)
2. 2 divides 48400 (48400 ÷ 2 = 24200) → pair (2, 24200)
3. 4 divides 48400 (48400 ÷ 4 = 12100) → pair (4, 12100)
4. 5 divides 48400 (48400 ÷ 5 = 9680) → pair (5, 9680)
5. 8 divides 48400 (48400 ÷ 8 = 6050) → pair (8, 6050)
6. 10 divides 48400 (48400 ÷ 10 = 4840) → pair (10, 4840)
7. 11 divides 48400 (48400 ÷ 11 = 4400) → pair (11, 4400)
8. 16 divides 48400 (48400 ÷ 16 = 3025) → pair (16, 3025)
9. 20 divides 48400 (48400 ÷ 20 = 2420) → pair (20, 2420)
10. 22 divides 48400 (48400 ÷ 22 = 2200) → pair (22, 2200)
11. 25 divides 48400 (48400 ÷ 25 = 1936) → pair (25, 1936)
12. 40 divides 48400 (48400 ÷ 40 = 1210) → pair (40, 1210)
13. 44 divides 48400 (48400 ÷ 44 = 1100) → pair (44, 1100)
14. 50 divides 48400 (48400 ÷ 50 = 968) → pair (50, 968)
15. 55 divides 48400 (48400 ÷ 55 = 880) → pair (55, 880)
16. 80 divides 48400 (48400 ÷ 80 = 605) → pair (80, 605)
17. 88 divides 48400 (48400 ÷ 88 = 550) → pair (88, 550)
18. 100 divides 48400 (48400 ÷ 100 = 484) → pair (100, 484)
19. 110 divides 48400 (48400 ÷ 110 = 440) → pair (110, 440)
20. 121 divides 48400 (48400 ÷ 121 = 400) → pair (121, 400)
21. 176 divides 48400 (48400 ÷ 176 = 275) → pair (176, 275)
22. 200 divides 48400 (48400 ÷ 200 = 242) → pair (200, 242)
23. 220 divides 48400 (48400 ÷ 220 = 220) → pair (220, 220)
24. Collect all unique values: {1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80, 88, 100, 110, 121, 176, 200, 220, 242, 275, 400, 440, 484, 550, 605, 880, 968, 1100, 1210, 1936, 2200, 2420, 3025, 4400, 4840, 6050, 9680, 12100, 24200, 48400} — total 45 divisors.
25. Sum: 1 + 2 + 4 + 5 + 8 + 10 + 11 + 16 + 20 + 22 + 25 + 40 + 44 + 50 + 55 + 80 + 88 + 100 + 110 + 121 + 176 + 200 + 220 + 242 + 275 + 400 + 440 + 484 + 550 + 605 + 880 + 968 + 1100 + 1210 + 1936 + 2200 + 2420 + 3025 + 4400 + 4840 + 6050 + 9680 + 12100 + 24200 + 48400 = 127813.

Nearby Examples

Related Operations for 48400

• Multiples of a Number — "outward" complement of divisors
• 48400 Prime Factorization — decompose into prime building blocks
• Find GCF of 48400 and another number
• Find LCM of 48400 and another number
• Is 48400 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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