A multiple is the product of a number and an integer.

A numerical factor is a factor that is an integer.

A square number is the product of two repeated integers.

A cube number is the product of three repeated integers.

A product is the result of two or more numbers multiplied together.

Checking understanding of factors, multiples, squares and cubes

Maths

This unit on factors, multiples, squares and cubes helps pupils build on their understanding that any positive integer can be expressed as a product of its factors. This skill is used in the next unit to explore multiplying and dividing with decimals.

In this unit, pupils learnt how to identify common factors and common multiples. in this unit, pupils build on this understanding to find the LCM and HCF

In this unit pupils develop their understanding of factors and multiples, then extend this knowledge to learn general divisibility tests for integers and develop strategies to determine the highest common factor and lowest common multiple of two or more integers.

Properties of number: factors, multiples, squares and cubes

Securing understanding of factors, multiples, squares and cubes

A common multiple is a number that is a multiple of two or more numbers.

Listing multiples

Divisibility is a number’s ability to be exactly divided by another number, leaving no remainder.

Divisibility tests for 2 and 3

Divisibility tests for 6 and 9

Divisibility tests for 5 and 10

Divisibility tests for 4 and 8

Square and cube numbers

A perfect square is the same as a square number.

A perfect cube is the same as a cube number.

Square and cube roots

The base is the number or term that has been multiplied by itself.

An integer exponent identifies how many times the base number has been multiplied by itself.

Power notation

Evaluate means to find the value of a numerical or an algebraic expression.

Powers and roots using a calculator

Listing factors

A prime number is an integer greater than one with exactly two factors.

Checking understanding of prime numbers

A composite number is an integer with more than two factors. All integers greater than 1 are either composite or prime

Prime factors are the factors of a number that are, themselves, prime.

Each composite number has a unique product of its prime factors.  i.e. there is only one unique way it can be written.

Expressing an integer as a product of its prime factors

A composite number is an integer with more than two factors.

Prime factors are factors of a number that are, themselves, prime.

An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication.

Calculating integers from their prime factor expressions

a method to find the prime factors of a given integer

The highest common factor of two or more integers  which can be divided by all other possible common factors

an abbreviation for highest common factor

Highest common factor

The lowest common multiple is the lowest number that is a multiple of two or more integers.

LCM is an abbreviation for lowest common multiple.

Lowest common multiple

HCF is an abbreviation for highest common factor.

LCM is an abbreviation for lowest common factor.

HCF or LCM

A square number is the product of two repeated integers

A cube number is the product of three repeated integers

A multiple is the product of a number and an integer

A numerical factor is a factor that is an integer

Properties of number: factors, multiples, squares and cubes

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These lessons will be removed by end of Summer Term 2025.