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Prime Factorisation
Shows a factor tree — for example 60 → 2 × 2 × 3 × 5.
Examples
Tap for an instant factorisationFactor tree
60 = 2 × 2 × 3 × 5
= 2² × 3 × 5
All the divisors of 60 (12):
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
How does this work?
A prime number is a whole number greater than 1 with no divisors other than 1 and itself — for example 2, 3, 5, 7, 11, 13. Every other number is called a composite number.
The Fundamental Theorem of Arithmetic says that every positive number greater than 1 can be broken down into prime factors in exactly one way (aside from the order). Each time, we look for the smallest prime factor, divide by it, and carry on — until only prime numbers remain as the leaves of the tree.
Three full worked examples
60
60 = 2 × 2 × 3 × 5(= 2² × 3 × 5)
72
72 = 2 × 2 × 2 × 3 × 3(= 2³ × 3²)
84
84 = 2 × 2 × 3 × 7(= 2² × 3 × 7)
Divisibility rules worth remembering
- Divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
- Divisible by 3 if the digit sum is divisible by 3 (e.g. 72 → 7+2=9 ✓).
- Divisible by 5 if the last digit is 0 or 5.
- Divisible by 9 if the digit sum is divisible by 9.
- Divisible by 10 if the last digit is 0.
💼 Where is this used?
- Simplifying fractions — dividing the numerator and denominator by their highest common factor.
- Finding the LCM (lowest common multiple) and HCF (highest common factor).
- Working out the number of divisors of a number directly from the powers of its prime factors.
- Cryptography (RSA) — based on how hard it is to factorise very large numbers.
- Checking primality and simplifying algebraic expressions.
How to use it
- Type a whole number between 2 and 10000.
- Click Factorise to see the factor tree.
- For a prime number, a single leaf is shown with the label "Prime".
- Pick an example below — it will be entered and factorised automatically.
Related tools
∩ HCF and LCM Calculator
Highest common factor (HCF) and lowest common multiple (LCM) — with Euclid's algorithm.
÷ Guided Long Division
Shows every step of long division — quotient, remainder, and bringing down the next digit.
½ Fractions Calculator
Add, subtract, multiply and divide fractions — with worked solutions.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specifications