Master prime numbers, prime factorization, and common factors with this 6-page worksheet pack. Ideal for Year 5, Year 6, and Key Stage 3 maths revision.

Help your students build a deep, conceptual understanding of number theory with this printable Prime Numbers and Prime Factorization Worksheet Pack. Instead of relying on brute-force multiplication or tedious long division, these exercises train learners to look structurally at numbers through digit sums, divisibility rules, and prime building blocks.
This resource contains 3 student practice worksheets and 3 complete answer key pages—fully worked out to save you valuable marking time!

What is Prime Factorization?
Prime factorization is the process of breaking down a composite number into a unique set of prime numbers that multiply together to give the original total. By teaching students to recognize these building blocks—and use index notation (exponents) like 2² • 5 • 7—they develop the critical algebraic foundations needed to calculate the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of larger integers without manual calculation.

What’s Included in This Resource?
• Worksheet 1: Prime Identification & Patterns: Students identify primes from a mixed number list, analyze why numbers ending in 5 are composite (except 5 itself), and use the digit-sum rule to discover patterns about multiples of 3.
• Worksheet 2: Listing Factors from Prime Powers: Students list all factors of numbers given in prime factorization form (such as 2 • 3 • 5) without needing to evaluate the actual number. It also includes multiple-choice divisibility checks.
• Worksheet 3: Finding Common Factors: Students compare two numbers in their prime factorization forms to isolate and list all of their common factors.
• Pages 4–6: Step-by-Step Answer Keys: Includes full solutions and structural breakdowns for every single question to encourage independent self-marking or quick teacher grading.

Curriculum and Age Suitability
• Primary (KS2): Highly relevant for Year 5 and Year 6 students mastering factors, multiples, prime identification up to 100, and initial prime power concepts.
• Secondary (KS3): Excellent for Year 7 and Year 8 students as a diagnostic tool, mastery extension task, intervention group resource, or formal exam revision.
• Adaptable Format: Perfect for whole-class lessons, independent desk work, maths secondary extensions, homework assignments, or structured test prep.