Factor Calculator
Factors are the whole numbers that divide a value exactly — the pairs behind every division that comes out clean. Students need them for simplifying and factorising, teachers for marking, and anyone scheduling or hashing for patterns that repeat. This calculator lists every factor of your number in order, counts them, and breaks the value into primes with proper exponents.
Enter values
Results
- All factors of 840
- 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
- Number of factors
- 32
- Prime factorisation
- 2³ × 3 × 5 × 7
How is the Factor calculated?
One field takes a whole number from 1 to 1,000,000, the cap that keeps the full list readable on one screen. The sweep runs from 1 up to √N, pairing each divisor with its partner (i × something = N) so nothing is counted twice, and the factors print in ascending order. The count follows, then the prime factorisation, obtained by dividing N by its smallest prime repeatedly.
Formula
A factor is any d where N mod d = 0, collected together with N ÷ d while i runs from 1 to √N. Prime factorisation divides N by 2 while it divides, then 3, 5 and upwards, recording exponents: 840 = 2³ × 3 × 5 × 7. The divisor count adds 1 to each exponent and multiplies — (3+1)(1+1)(1+1)(1+1) = 32.
Example
Take 840: the sweep to √840 ≈ 28.98 collects 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24 and 28, each matched with its partner, giving 32 factors in all. Repeated division yields 840 = 2³ × 3 × 5 × 7, and (3+1)(1+1)(1+1)(1+1) confirms the count. A prime such as 97 defeats the sweep entirely: only 1 and 97 divide it.
Things to remember
Two numbers sharing no factor beyond 1 — 97 and 100, say — are co-prime, a property that matters whenever fractions are simplified or cycles synchronised. The prime factorisation row is the durable part: it never changes however you group the factors, and it feeds straight into least common multiple and HCF work.
Frequently Asked Questions
How do you find all the factors of a number?
Divide the number by every integer up to its square root and record each divisor that fits exactly, along with its matching partner. For 24 that yields 1, 2, 3, 4, 6, 8, 12 and 24 — eight factors sitting in pairs that always multiply back to 24.
How many factors does a number have?
Read them off its prime factorisation: add 1 to each exponent and multiply the results. Since 840 = 2³ × 3 × 5 × 7, its factor count is (3+1)(1+1)(1+1)(1+1) = 32. Prime numbers are the simple case, carrying exactly two factors — 1 and themselves.
What is the difference between a factor and a multiple?
A factor divides the number exactly and never exceeds it, while a multiple sits on the number's times table and never falls below it. Factors of 12 run from 1 to 12; multiples run 12, 24, 36 onwards, and the LCM page handles that second direction.
Why is the calculator limited to 1,000,000?
Because it prints every factor in full. The sweep itself is quick — it stops at the square root — but numbers with hundreds of divisors would spill a result too long to read. For primality at far larger sizes, the prime number page keeps working up to 10¹².
Related Calculators
- Prime Number CalculatorMath & ArithmeticCheck whether a number is prime, see its smallest prime factor and find the next prime that follows it.
- LCM CalculatorMath & ArithmeticFind the least common multiple of two whole numbers, with their GCD and the identity that links the two.
- HCF CalculatorMath & ArithmeticFind the highest common factor of two numbers, shown with every division performed by Euclid's algorithm.
- Fraction CalculatorMath & ArithmeticAdd, subtract, multiply or divide two fractions and get the answer simplified, plus its decimal and percentage forms.