Prime & Composite Numbers, Prime Factorization, HCF LCM Worksheets & Keys

A collection of three worksheets on the following: * Prime numbers and prime factorization. The exercises require to decide whether some given numbers are prime or not and reach some conclusions about prime numbers, find the factors of a number given its prime factorization, find the common factors of two numbers given their prime factorizations and find the prime factorization of a number using repeated division. * Prime factorization. The exercises require to find the prime factorization of a number using repeated division. * Highest common factor and lowest common multiple. The exercises require to find the prime factorization of some numbers and then use it to find their HCF and their LCM. Detailed solutions are included. Master number theory with this ultimate 34-page maths worksheet bundle! Covers prime and composite properties, prime factorisation, HCF, and LCM. Perfect for Year 5, Year 6, and Key Stage 3 (Year 7) classwork, homework, or revision. Includes complete, step-by-step division ladder worked solutions to make marking completely effortless! ________________________________________ Looking for a comprehensive, rigorous, and completely print-and-go bundle to help your students master number theory? This Prime & Composite Numbers, Prime Factorisation, HCF LCM Worksheets & Keys pack is the ultimate classroom toolkit. Moving smoothly from foundational properties to advanced Key Stage 3 maths concepts, this 34-page collection shifts students away from simple guessing and guides them toward deep conceptual mastery. **Topics Covered in This Pack** • Prime vs. Composite Properties: Exploring consecutive primes, twin primes, and patterns in ending digits. • Mathematical Reasoning: Expressing numbers as sums of primes and exploring number theory rules. • Advanced Factor Analysis: Listing all factors from given prime factorisations without calculating the base products first. • Prime Factorisation Drills: 30 structured problems ranging from simple two-digit numbers up to challenging three-digit values (such as 408 and 945). • HCF & LCM Mastery: Utilizing prime factor products and index notation to quickly calculate Highest Common Factors and Lowest Common Multiples for large number pairs (up to 720). **What Is Included in This Download?** • Comprehensive Student Worksheets: Highly structured, cleanly organized problem sets that progressively increase in difficulty to build student confidence. • Complete, Step-by-Step Worked Solutions: Not just a standard list of final answers! The key explicitly models full division ladders, factor listings, and exponential expansions to make student self-correction or teacher marking completely stress-free. **Why Teachers Love This Resource** • Zero Prep Required: Just choose your section, print the pages, and hand them out immediately to your classes. • Built-In Differentiation: Perfect for scaffolding skills for struggling learners or providing robust extension challenges for high-ability pupils. • Explicit Workings: The visual division ladders in the keys make it incredibly easy for students to spot exactly where they made an error. **Curriculum Alignment** • UK National Curriculum (KS2 / KS3): Fully covers core curriculum objectives for identifying factors, multiples, prime numbers, prime factor products using index laws, and computing the Highest Common Factor (HCF) and Lowest Common Multiple (LCM). ________________________________________