HCF is an abbreviation for highest common factor.

LCM is an abbreviation for lowest common multiple.

Prime factorisation is a method to find the prime factors of a given integer.

Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.

Checking and securing understanding of LCM and HCF

Maths

Checking and securing understanding of converting between fractions and decimals

Checking and securing understanding of calculating with fractions and decimals

Checking and securing understanding of prime factorisation

Checking and securing understanding of roots and integer indices

Checking and securing understanding of calculations involving negative numbers

The laws of indices - multiplication

The laws of indices - division

The laws of indices - raising a power to a power

The laws of indices - negative and zero exponents

Problem solving with the laws of indices

In this unit, pupils formalised their understanding of the index laws. This understanding will allow them to perform calculations with values written in standard form more efficiently.

The conditions for standard form mean that pupils have explored how different powers of 10 can be written in the prior unit. In this unit, this understanding is generalised and the index laws formalised.

In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.

Arithmetic procedures: index laws

What is the lowest common multiple of 32 and 48? 

What is the lowest common multiple of 32 and 50? 

What is the lowest common multiple of 30 and 48? 

What is the highest common factor of 32 and 48? 

What is the highest common factor of 32 and 50? 

What is the highest common factor of 32, 12 and 48? 

What number is written as $$2^2 × 7 × 19$$ as a product of its prime factors? 

What number is written as $$2^4 × 3 × 17$$ as a product of its prime factors? 

What number is written as $$2^2 × 3^3 $$ as a product of its prime factors? 

Which of these is a prime factor of 10908? 

Which of these is the prime factorisation of 620? 

Which of these is the prime factorisation of 184? 

Starter Quiz

What number is written as $$2^2 × 7 × 19$$ as a product of its prime factors?