HCF, LCM & Prime Factorisation Worksheets | Word Problems & Answer Keys
A collection of three worksheets on HCF and LCM. The exercises require to find the prime factorisation of a set of 2 or 3 numbers using repeated division and use it to evaluate their HCF and their LCF, decide whether a given pair of numbers are relatively prime (coprime), simplify fractions as much as possible by dividing their numerator and denominator by their HCF , add or subtract pairs of fractions after changing their denominator and using the LCM of the original denominators and solving word problems using the highest common factor and the lowest common multiple. Detailed solutions are included.
Master HCF, LCM, and prime factorisation with this comprehensive, print-and-go maths worksheet pack! Perfect for Year 5, Year 6, and Key Stage 3 (Year 7) classwork, homework, or revision. Features structured calculation drills, coprime logic, and real-world word problems alongside full step-by-step worked solutions!
**Topics Covered in This Pack**
• Prime Factorisation Drills: Breaking down numbers into prime factor products using standard expansion and index notation/laws.
• Core HCF & LCM Calculations: Structured extraction drills featuring double and triple-number sets up to 846 (such as finding common factors for 273, 585, and 735).
• Coprime / Relatively Prime Logic: Identifying number pairings that share no common factors other than 1.
• Real-World Word Problems: Solving practical distribution, grouping, and scheduling scenarios.
• HCF Distribution Scenarios: Calculating identical packages of pens and notebooks, or matching multi-coloured rose bouquets.
• LCM Simultaneous Events: Tracking scheduling overlaps for music lessons, dental visits, and doctor rotations.
• LCM Equal Packing: Matching packages of items like t-shirts and trousers, or balancing different sizes of bakery trays.
**What Is Included in This Download?**
• High-Quality Student Worksheets: Cleanly formatted problem sets designed with an organised layout for clear student calculations.
• Detailed Step-by-Step Worked Solutions: Not just a standard list of final answers! Every single problem includes full written logic, detailed factor lists, prime factor products, and visual division ladders to make teacher marking or student self-correction completely effortless.
**Why Teachers Love This Resource**
• Zero Prep Required: Simply select your target pages, print, and distribute immediately to your classes.
• Highly Visual Answer Keys: The keys explicitly lay out prime factorisation paths and visual division steps, making it easy for students to isolate exactly where they made an error.
• Built-In Differentiation: Features straightforward baseline pairs for struggling learners alongside complex triple-digit challenges to extend high-ability pupils.
**Curriculum Alignment**
• UK National Curriculum (Upper KS2 / KS3): Fully covers core curriculum objectives for identifying factors, multiples, prime numbers, highest common factors, lowest common multiples, and prime factor products using index laws in abstract and contextual word problems.
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