Multiples, Factors, Primes and Squares

Students learn how to find common multiples and factors pairs of numbers and algebraic terms.  By exploring the factor properties of different types of numbers students are introduced to prime and square numbers.

This unit takes place in Year 7 Term 2 and follows on from using place value.

Multiples, Factors, Primes and Squares Lessons

Prerequisite Knowledge

  • Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
  • Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
  • Establish whether a number up to 100 is prime and recall prime numbers up to 19
  • Identify common factors, common multiples and prime numbers

Key Concepts

  • A multiple of a number or term is found by multiplying it by any integer or other term.
  • A factor of a number is an integer or term that will divide exactly into that number or term.
  • A prime number has exactly two factors.  A common misconception is describe a prime as a number that will divide by 1 and itself.  This is incorrect as it will lead 1 itself to be prime.
  • Any number can be written as a product of its prime factors.  More able students should write prime factors using index notation.
  • The highest common factor of a set of numbers or terms is the largest number or term that is common to all exponents.
  • A square number can be imagined as the area of a square.  The square root would be the length of a square when the area is known.

Working mathematically

Develop fluency

  • Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots.
  • Select and use appropriate calculation strategies to solve increasingly complex problems.
  • Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships.

Reason mathematically

  • Extend their understanding of the number system; make connections between number relationships, and their algebraic representations

Solve problems

  • Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content


  • Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property
  • Use conventional notation for the priority of operations, including brackets, powers, roots


  • simplify and manipulate algebraic expressions to maintain equivalence by:
    • collecting like terms
    • multiplying a single term over a bracket
    • taking out common factors
    • expanding products of two or more binomials

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