Maths Help UK

Prime factor decomposition

Break any number into its prime factors using a factor tree. Year 7-8.

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Every whole number greater than 1 is either prime or can be written as a product of primes (the Fundamental Theorem of Arithmetic). The factor-tree method splits the number repeatedly until only primes remain.

Worked examples
60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
72 = 2³ × 3².
Useful for HCF and LCM calculations. See the LCM/HCF page.
Related: LCM and HCF Squares and cubes Indices (introduction) Standard form

Frequently asked questions

Is 1 prime?
No — the modern definition excludes 1 so the Fundamental Theorem gives a unique factorisation.
Why use index notation?
Compact and useful: 360 = 2³ × 3² × 5 reveals structure used in LCM/HCF.