Primes, factors and prime factor trees
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 7 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- The building blocks
- What is a prime number?
- Is it prime? A quick test
Read the transcript of the teaching part
Last time
Before we start: last time, in The four operations and negative numbers, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
The building blocks
Every whole number is built from a few special numbers, the way every word is built from letters. Those building blocks are the primes. Today you will find them, list the factors of any number, and break a number into its prime factors with a tree.
What is a prime number?
A factor of a number divides into it exactly, with nothing left over. A prime number has exactly two factors: one, and itself. So two, three, five, seven, eleven, thirteen are the first primes. One is not prime, because it has only one factor. And two is the only even prime.
Is it prime? A quick test
To test a number, try dividing it by two, three, five, seven in turn. You only need to try primes up to its square root. Is ninety-one prime? It is not even, and its digits sum to ten, so three fails. But seven times thirteen is ninety-one. Is ninety-seven prime? Seven times thirteen is ninety-one, and seven times fourteen is ninety-eight. Nothing fits, so it is prime.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Primes, HCF and LCM.
The whole chapter: Numbers and the Four Operations.
Chapter 1: Number
- Number families, reciprocals and ordering 6 min
- The four operations and negative numbers 5 min
- Primes, factors and prime factor trees 5 min
Also for O Level Maths 4024
Which topics come up most in O Level Maths 4024 past papers, counted from every paper since 2004.