How it works
Find all factors and factor pairs of a number.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
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?number=NumberNumber · Optional · Default: 60
Outputs
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resultResultText · Primary output
result contains the calculator’s complete rendered result area, including its visible result cards, tables, charts, and messages.
Discover all divisors and factor pairs of a number
Description
The Factor Calculator is a comprehensive utility for exploring the divisibility of integers. It identifies every number that can divide your input without leaving a remainder. Beyond just a simple list, it organizes results into Factor Pairs, showing you exactly which two numbers multiply together to create your target value.
Inputs
- Number: The positive integer you wish to analyze.
Outputs
- Total Factor Count: How many unique divisors the number has.
- All Factors: A sorted list of every divisor from 1 to the number itself.
- Factor Pairs: A visual list of multiplication pairs (e.g., $1 \times 60$, $2 \times 30$, etc.).
Chart
- N/A: This tool provides an organized numeric grid of results.
“Good to Know”
- Prime vs. Composite: If a number has exactly two factors (1 and itself), it is a Prime number. If it has more, it is a Composite number.
- Square Numbers: If a number is a “perfect square” (like 16 or 25), it will have an odd number of factors because its square root multiplies by itself.
- The “Factor of 1”: Every positive integer has at least two factors: 1 and the number itself.
Examples
Example 1: Composite Number (60)
- Input: 60
- Output:
- Count: 12
- Pairs: 1×60, 2×30, 3×20, 4×15, 5×12, 6×10
Example 2: Prime Number (13)
- Input: 13
- Output:
- Count: 2
- Factors: 1, 13
Example 3: Square Number (25)
- Input: 25
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- Output:
- Count: 3
- Pairs: 1×25, 5×5