Factor Calculator
Analyze any positive whole number to find its unique divisors, factor pairs, prime factorization exponents, and construct a recursive factor tree.
Note: Inputs are clamped between 1 and 1,000,000 to prevent CPU page lockups during factor factorization.
Number Taxonomy Profile
Factor Pairs Ledger
| Pair Index | Factor A | Factor B | Equation |
|---|---|---|---|
| Pair #1 | 1 | 36 | 1 × 36 = 36 |
| Pair #2 | 2 | 18 | 2 × 18 = 36 |
| Pair #3 | 3 | 12 | 3 × 12 = 36 |
| Pair #4 | 4 | 9 | 4 × 9 = 36 |
| Pair #5 | 6 | 6 | 6 × 6 = 36 |
Recursive Factor Tree Visualization
Decomposing Whole Numbers
Factors are the building blocks of integers. A **factor** (or divisor) is a whole number that divides another number evenly, leaving zero remainder. For instance, the factors of 15 are 1, 3, 5, and 15.
Prime vs. Composite Numbers
Every positive integer greater than 1 is classified as either:
- Prime Number: Divisible only by 1 and itself (e.g. 2, 3, 5, 7, 11, 13).
- Composite Number: Has divisors beyond 1 and itself, meaning it can be built by multiplying smaller factors.
Proper Divisor Sums & Number Theory Metrics
Number theory profiles integers based on the sum of their **proper divisors** (which are all positive divisors excluding the number itself). By comparing this proper sum to the number, we group it into three categories:
- Perfect Number: The proper sum equals the number exactly ($S = N$). For example, 6 (proper divisors 1, 2, 3 sum to 6).
- Abundant Number: The proper sum exceeds the number ($S > N$). For example, 12 (proper sum $1+2+3+4+6 = 16 > 12$).
- Deficient Number: The proper sum is less than the number ($S < N$). For example, 8 (proper sum $1+2+4 = 7 < 8$).
Frequently Asked Questions
What is the difference between a factor and a prime factor?
A factor is any integer that divides a given number evenly without a remainder. A prime factor is a factor that is also a prime number (divisible only by 1 and itself).
What is a perfect number?
A perfect number is a positive integer that is equal to the sum of its proper divisors (all positive factors excluding the number itself). The smallest perfect number is 6.
How is a factor tree generated?
A factor tree is built by dividing the starting number into any two factor components. Any prime factor is kept, while the composite factor is split further recursively until only prime numbers remain.
Does this find prime factorization?
Yes. Get all factors, factor pairs, and prime factorization trees for any number.