Factors, multiples, primes and counting
Pages
Factors and factor pairs
Listing every factor of a number in pairs, so none is missed or repeated.
Multiples and divisibility tests
The multiples of a number, and the tests for divisibility by 2, 3, 4, 5 and 9.
Primes and testing for primality
What makes a number prime, why 1 is not, and trial division up to the root.
Prime factorisation
Factor trees and repeated division, index form, and why the primes are unique.
Highest common factor
Taking each shared prime to the lower index, and what the HCF means.
Lowest common multiple
Every prime to the higher index, and why the LCM is not always the product.
HCF and LCM from a Venn diagram
The Venn method for two or three numbers, and HCF times LCM as the product.
Choosing HCF or LCM in context
Deciding which a worded problem needs: coinciding events or equal shares.
Squares and cubes from prime factors
The smallest multiplier that turns a number into a perfect square or cube.
Counting a number’s factors
Counting a number’s factors from the indices in its prime factorisation.
Systematic listing
Listing every outcome once in a fixed order, and deciding whether order matters.
The product rule for counting
Multiplying the choices at each stage, including arrangements without reuse.
Practice
Factors and factor pairs
Listing every factor of a number in pairs, so none is missed or repeated.
PracticeMultiples and divisibility tests
The multiples of a number, and the tests for divisibility by 2, 3, 4, 5 and 9.
PracticePrimes and testing for primality
What makes a number prime, why 1 is not, and trial division up to the root.
PracticePrime factorisation
Factor trees and repeated division, index form, and why the primes are unique.
PracticeHighest common factor
Taking each shared prime to the lower index, and what the HCF means.
PracticeLowest common multiple
Every prime to the higher index, and why the LCM is not always the product.
PracticeHCF and LCM from a Venn diagram
The Venn method for two or three numbers, and HCF times LCM as the product.
PracticeSquares and cubes from prime factors
The smallest multiplier that turns a number into a perfect square or cube.
PracticeThe product rule for counting
Multiplying numbers of choices for combined selections.
PracticePrime factorisation review
Divisibility, spotting primes, and reading squares.
PracticeHCF and LCM review
HCF and LCM from prime factors, including three numbers and worded decisions.
PracticeCounting by listing review
Counting factor pairs, arrangements and choices exactly by systematic listing.