Prime Factorization GCF LCM HCF Worksheet with Answers

A worksheet on prime factorization, GCF and LCM. The exercises require to:

• decide whether some given numbers are prime or not
• express a number as a product of its prime factors using repeated division
• find factors of a number given its prime factorization
• find the GCF and and the LCM of two or three numbers using their prime factorizations
• solve word problems involving the GCF and and the LCM
  There are four pages of exercises. Detailed solutions are included.

Looking for a no-prep, print-and-go resource to help your students master prime factors and common multiples? This comprehensive math worksheet delivers structured, clean, and highly effective practice layout templates designed to build confidence in Middle School Math, Pre-Algebra, Key Stage 3 (KS3), and Upper Elementary classrooms.
Whether you need sub plans, independent homework, guided class practice, or structured math intervention, this worksheet gives your students the exact scaffolding they need to solve complex number theory problems.

What’s Included in This Worksheet?
This downloadable PDF features 11 multi-part problems spread across 4 student practice pages, complete with fully worked-out teacher answer keys:

• Core Skill Practice (Questions 1-2): Identifying prime vs. composite numbers (up to 143) and expressing values as a product of prime factors.
• Advanced Number Theory (Questions 3-4): Using prime factorization strings to deduce composite divisors and test complex divisibility rules.
• GCF, HCF & LCM Calculations (Question 5): Finding the Greatest Common Factor / Highest Common Factor and Lowest Common Multiple for groups of two and three numbers.
• Real-World Word Problems (Questions 6-7): Application problems focusing on satellite orbital alignments (LCM) and cutting ribbon lengths evenly (GCF/HCF).
• Algebraic Constraint Puzzles (Questions 8-11): Rigorous challenge problems where students must solve for unknown variables (x and y) using given GCF and LCM conditions.

Why Educators Choose Mathamaniacs Resources:

• Zero Prep Required
• Step-by-Step Answer Keys Included
• Clutter-Free Visual Design
• Versatile Classroom Use

Target Audience & Curriculum Fit:

• Grades / Key Stages: 6th Grade, 7th Grade, 8th Grade / Key Stage 3 (KS3 Maths)
• Core Topics: Prime Factorization, Product of Prime Factors, Greatest Common Factor (GCF), Highest Common Factor (HCF), Least Common Multiple (LCM), Lowest Common Multiple, Divisibility Rules, Word Problems.

Key Words:
prime factorization, gcf worksheet, hcf practice, lcm word problems, highest common factor, lowest common multiple, prime factors, no prep math, 6th grade math, ks3 maths, prealgebra review