Number · Integers, powers & roots
Chapter 1 · 3
The idea
Prime factorisation
Why every whole number breaks into a unique product of primes, how to find it with a factor tree, and how the prime form answers divisibility and square-number questions instantly.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Number · Integers, powers & roots
Prime factorisation
Why every whole number breaks into a unique product of primes, how to find it with a factor tree, and how the prime form answers divisibility and square-number questions instantly.
Why it works
One number, one fingerprint
Exam papers ask it plainly — *"write as a product of prime factors in index form" — and then ask stranger things off the back of it: show that is square, what's the smallest number to multiply by to make a square?* All of it is one skill. Primes are the atoms of the whole numbers: a prime has exactly two factors (itself and ), and every whole number above is a product of primes in exactly one way. For our running number,Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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