Grade 4 · Unit 1: Number and place value

HCF and LCM

Factor trees, common factors and common multiples.

Equal packs

A teacher has 12 pencils and 18 erasers to put in gift bags. Every bag must be the same, with nothing left over. The biggest number of bags is the highest common factor of 12 and 18.

Factor trees

Split a number into two factors, again and again, until every branch ends in a prime. This is a factor tree. 36 = 2 × 2 × 3 × 3 – these are its prime factors.

Listing common factors and multiples

List the factors of each number. The ones in both lists are common factors. The biggest is the HCF: 6. List multiples to find the lowest common multiple: 12, 24, 36 and 18, 36 → LCM = 36.

The division method

Divide both numbers by a prime that goes into both. Repeat. Multiply the primes on the left: that is the HCF. Multiply the left primes and the numbers left at the bottom: that is the LCM.

Square and triangular numbers

Square numbers make squares: 1, 4, 9, 16, 25. Triangular numbers make triangles: 1, 3, 6, 10, 15. Add the next counting number each time: 1, +2, +3, +4 …

What I learnt

• I can draw factor trees.
• I can find common factors and common multiples.
• I can find the HCF and LCM by the division method.
• I know square and triangular numbers.