Divisors of 400: All 15 Factors
Quick Answer
400 has 15 divisors (factors): 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400.
Sum: 961. 400 is a perfect square (√400 = 20).
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 400
The number 400 has 15 divisors:
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Divisor Pairs of 400
Each pair multiplies to 400:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 400 | = | 400 |
| 2 | × | 200 | = | 400 |
| 4 | × | 100 | = | 400 |
| 5 | × | 80 | = | 400 |
| 8 | × | 50 | = | 400 |
| 10 | × | 40 | = | 400 |
| 16 | × | 25 | = | 400 |
| 20 | × | 20 | = | 400 |
Note: the last pair has identical factors (20 × 20) because 400 is a perfect square.
Number of Divisors
The number 400 has 15 divisors, written as τ(400) = 15 in number theory.
⚡ Notice: 400 has an odd number of divisors — this means 400 is a perfect square (√400 = 20).
Sum of Divisors
σ(400) = 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 40 + 50 + 80 + 100 + 200 + 400 = 961
Prime Factorization of 400
Properties of 400
- 400 is composite.
- 400 is a perfect square (√400 = 20).
- Number of divisors: 15.
- Sum of divisors: 961.
Common Divisors with Another Number?
Looking for the divisors that 400 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 400
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √400 ≈ 20.00. If i divides 400, then both i and 400/i are divisors.
- 1 divides 400 (400 ÷ 1 = 400) → pair (1, 400)
- 2 divides 400 (400 ÷ 2 = 200) → pair (2, 200)
- 4 divides 400 (400 ÷ 4 = 100) → pair (4, 100)
- 5 divides 400 (400 ÷ 5 = 80) → pair (5, 80)
- 8 divides 400 (400 ÷ 8 = 50) → pair (8, 50)
- 10 divides 400 (400 ÷ 10 = 40) → pair (10, 40)
- 16 divides 400 (400 ÷ 16 = 25) → pair (16, 25)
- 20 divides 400 (400 ÷ 20 = 20) → pair (20, 20)
- Collect all unique values: {1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400} — total 15 divisors.
- Sum: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 40 + 50 + 80 + 100 + 200 + 400 = 961.
Nearby Examples
Related Operations for 400
- Multiples of 400 — "outward" complement; M is a multiple of 400 ⇔ 400 is a divisor of M
- 400 Prime Factorization — decompose into prime building blocks
- Find GCF of 400 and another number
- Find LCM of 400 and another number
- Is 400 a perfect square? (odd divisor count ⇔ yes)
See also our tables of divisors:
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.
Divisors Calculation Examples
Find all divisors of these numbers:
Related Calculators
- Multiples of a Number — "outward" complement
- Prime Factorization — product of prime divisors
- Greatest Common Factor (GCF) — largest common divisor of 2+ numbers
- Least Common Multiple (LCM) — smallest common multiple
- Is N a Perfect Square? — odd divisor count check