Master factors, multiples, and prime or composite numbers with this comprehensive, no-prep maths worksheet! Perfect for Key Stage 2 and Key Stage 3 (KS2/KS3) students in Years 5, 6, and 7 learning to find factor pairs, list multiples, and reason through conceptual true or false questions. Full teacher solutions are included!

Are your students getting tripped up separating factors from multiples? Help them gain absolute clarity with this comprehensive Factors and Multiples Practice Worksheet!
This resource features a highly structured layout that moves students from basic computation to deep, conceptual reasoning. It is specifically designed to expose common maths misconceptions—such as confusing factors with multiples or assuming all even numbers are composite.

What’s Included:
• Section 1: Finding All Factors: 11 targeted problems ranging from single digits to 100, requiring students to find complete factor pairs (Numbers included: 6, 7, 8, 9, 12, 18, 24, 31, 50, 72, 100).
• Section 2: Listing Multiples: Focused practice finding the first 5 multiples for a variety of numbers (Numbers included: 3, 5, 7, 11, 20, 25, 33, 50).
• Section 3: Factor Density Analysis: An analytical question asking students to compare and find which number holds the most factors (Choosing between 10, 21, 36, 40, and 49).
• Section 4: 14 Concept-Heavy True or False Statements: Critical thinking questions designed to test deep understanding of number properties (e.g., “all the multiples of 4 are even”, “every number has infinitely many multiples”).
• Complete Teacher Solutions Key: Includes full factor lists, multiples, and detailed correction notes for false statements—perfect for quick marking, self-assessment, or supply teacher cover lessons!

Core Skills Covered:
• Identifying complete factor pairs for numbers up to 100.
• Generating multiples systematically.
• Differentiating between prime and composite properties.
• Analyzing mathematical rules regarding even/odd factors and multiples.

Classroom Versatility:
• Daily Homework: Assign specific sections to reinforce your daily lesson.
• Maths Rotations & Extension Tasks: Great for independent work or peer-led team practice.
• Revision & Diagnostics: Use the true/false matrix as an excellent starter or plenary activity before tackling fractions, lowest common multiples (LCM), or highest common factors (HCF).

Curriculum Standards Alignment:
• UK National Curriculum (Key Stage 2 & 3 Mathematics): Aligned with upper primary and early secondary objectives to identify multiples and factors, including finding all factor pairs of a number, identifying common factors of two numbers, knowing and using the vocabulary of prime numbers, prime factors, and composite numbers.