Two worksheets on finding the HCF and LCM using prime factorisation. Detailed solutions are provided.

HCF and LCM worksheets using prime factorisation with fully worked solutions. Perfect for KS3 maths classes, GCSE foundation revision, or home learning.

Save hours of planning and grading time with this comprehensive, print-and-go worksheet pack. This resource focuses on mastering the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) through prime factor decomposition using product of primes and index notation.

Mathematical Context & Definition
Prime factorisation (or prime decomposition) is the process of breaking down a composite number into a product of its prime factors. By expressing numbers in this format, students can easily identify common factors to calculate the Highest Common Factor (HCF) and compile prime factors to find the Lowest Common Multiple (LCM). This resource provides extensive practice to reinforce this fundamental number system skill.

Key Features of This Resource:
• Ready to Print: Completely prepped and structured to reduce your marking workload.
• Scaffolded Rigor: Problems scale from basic integers up to challenging three-digit integers (including numbers like 720 and 525) to stretch high-achieving students.
• Detailed Step-by-Step Solutions: Every question features a handwritten-style division ladder breakdown so pupils can cross-check their own logic, making it ideal for self-assessment, homework, or cover work.

What is Included in the Download?
• Task Sheet 1: Writing composite numbers as products of their prime factors using index notation.
• Task Sheet 2: Determining the HCF and LCM for given pairs of numbers.
• Answer Booklet: Full, explicit step-by-step worked keys for all activities.

Target Student Audience:
• Key Stage 3 (KS3 Maths): Perfect for Year 7, Year 8, and Year 9 core number skills.
• GCSE Mathematics: Excellent for Foundation tier revision or Higher tier remediation.
• Functional Skills Mathematics: Level 1 and Level 2 number operations.