Divisors of 100: All 9 Factors
Quick Answer
100 has 9 divisors (factors): 1, 2, 4, 5, 10, 20, 25, 50, 100.
Sum: 217. 100 is a perfect square (√100 = 10).
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 100
The number 100 has 9 divisors:
1, 2, 4, 5, 10, 20, 25, 50, 100
Divisor Pairs of 100
Each pair multiplies to 100:
| Factor 1 | × | Factor 2 | = | Product |
|---|---|---|---|---|
| 1 | × | 100 | = | 100 |
| 2 | × | 50 | = | 100 |
| 4 | × | 25 | = | 100 |
| 5 | × | 20 | = | 100 |
| 10 | × | 10 | = | 100 |
Note: the last pair has identical factors (10 × 10) because 100 is a perfect square.
Number of Divisors
The number 100 has 9 divisors, written as τ(100) = 9 in number theory.
⚡ Notice: 100 has an odd number of divisors — this means 100 is a perfect square (√100 = 10).
Sum of Divisors
σ(100) = 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 = 217
Prime Factorization of 100
Properties of 100
- 100 is composite.
- 100 is a perfect square (√100 = 10).
- Number of divisors: 9.
- Sum of divisors: 217.
Common Divisors with Another Number?
Looking for the divisors that 100 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 100
An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √100 ≈ 10.00. If i divides 100, then both i and 100/i are divisors.
- 1 divides 100 (100 ÷ 1 = 100) → pair (1, 100)
- 2 divides 100 (100 ÷ 2 = 50) → pair (2, 50)
- 4 divides 100 (100 ÷ 4 = 25) → pair (4, 25)
- 5 divides 100 (100 ÷ 5 = 20) → pair (5, 20)
- 10 divides 100 (100 ÷ 10 = 10) → pair (10, 10)
- Collect all unique values: {1, 2, 4, 5, 10, 20, 25, 50, 100} — total 9 divisors.
- Sum: 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 = 217.
Nearby Examples
Related Operations for 100
- Multiples of 100 — "outward" complement; M is a multiple of 100 ⇔ 100 is a divisor of M
- 100 Prime Factorization — decompose into prime building blocks
- Find GCF of 100 and another number
- Find LCM of 100 and another number
- Is 100 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