Factors, multiples, prime numbers and composite numbers

Spine 2: Multiplication and Division – Topic 2.21

Primary KS2 Year 5
Mastery PD Materials


Identify properties of factors and multiples including square and prime numbers, composite numbers, common and prime factors, and common multiples. Use factor pairs to solve problems efficiently.

Teaching points

  • Teaching point 1: Factors are positive integers that can be multiplied together to equal a given number.
  • Teaching point 2: Systematic methods can be used to find all factors of a number; factors come in pairs; all positive integers have an even number of factors apart from square numbers, which have an odd number of factors; numbers with more than two factors are called composite numbers.
  • Teaching point 3: Prime numbers are positive integers that have exactly two factors.
  • Teaching point 4: A common factor is a factor that is shared by two or more numbers. A prime factor is a factor that is also a prime number.
  • Teaching point 5: A multiple of a number is the product of that number and an integer; a common multiple is a multiple that is shared by two or more numbers.
  • Teaching point 6: The factor pairs of ‘100’ can be used to support efficient calculation.