Factor Calculator
Every factor, every factor pair, the prime factorization and a visual factor tree for any positive integer up to 10 million.
What is a factor?
A factor of an integer n is any positive integer that divides n with no remainder. Factor pairs are the two-number products that reconstruct n; the prime factorization is the unique way to write n as a product of primes. This calculator returns all three views at once, plus a visual factor tree.
Factor calculator, piece by piece
Each card explains one section of the output above — the full factor list, factor pairs, the prime factorization, and the factor tree diagram.
All factors — every divisor of n
The first result box lists every positive integer that divides your number evenly. Under the hood the calculator only tests candidates up to √n — each hit gives two factors at once (the divisor and the quotient), which is why the list appears instantly even for seven-digit inputs.
Factor pairs — rectangles that make n
The second result box groups the factors into pairs (a, b) with a × b = n. Each pair is one way to arrange n items into a rectangle. Perfect squares get a self-pair like (10, 10); the calculator prints it once so the list stays clean.
Prime factorization — how the calculator builds it
The third box shows n written as a product of primes. The tool works by peeling off the smallest prime that fits, dividing, and repeating on the quotient until it hits a prime — the sequence of divisors is the factorization. It's unique for every integer above 1.
Factor tree — the picture at the bottom
The tree diagram at the bottom of the output is the same factorization drawn as branches: split into any two factors, then split any composite leaf again, and keep going until every leaf is a prime. Primes are highlighted in the theme colour.
Features of this calculator
- Lists all factors of the number in ascending order
- Shows every factor pair (a, b) with a × b = n
- Gives the prime factorization as a plain multiplication
- Renders a visual factor tree that matches the site theme
- Handles inputs up to 10,000,000 without blocking the browser
Frequently asked questions
+How do I find all factors of a number?
Test every integer from 1 up to √n. Each one that divides evenly gives you two factors: the divisor itself and the quotient. Collecting those pairs gives the full list.
+What is a factor tree?
A diagram that splits a number into two factors, splits any composite factors again, and keeps going until every leaf is prime. The leaves are the prime factorization.
+Is 1 a prime factor?
No. 1 is a factor of every integer, but primes are defined as integers greater than 1, so 1 never appears in a prime factorization.
+Why is there an upper limit on the input?
Above about 10 million, browser-side trial division starts to lag noticeably. Larger inputs need specialized algorithms and dedicated servers rather than a single tab of JavaScript.