Factors, Multiples, Indices, Roots and Standard Form

Prior learning: Year 7 Autumn 2; Year 8 Autumn 2

Topic Foundation Higher
Factors, Multiples, Indices, Roots and Standard Form

Exemplification questions


Calculate factors and multiples

List the prime factors of a number as a product

Calculate the HCF and LCM of numbers or expressions

Calculate powers and roots

Use the three laws of indices

Change between normal notation and standard form

Calculate with numbers in standard form

Use the laws of indices for fractional and negative powers

Simplify surds and expressions involving surds

Rationalise the denominator of fractions

Perform harder calculations with numbers in standard form


Students should be able to:

  • identify multiples, factors and prime numbers from lists of numbers
  • write out lists of multiples and factors to identify common multiples or common factors of two or more integers
  • write a number as the product of its prime factors and use formal (eg using Venn diagrams) and informal methods (eg trial and error) for identifying highest common factors (HCF) and lowest common multiples (LCM)
  • work out a root of a number from a product of prime factors.

Students will be expected to apply index laws to simplify numerical and algebraic expressions.