Highest Common Factors (HCF) of Algebraic Terms WORKSHEET

Guide students through understanding and finding the highest common factors (HCF) of algebraic terms step by step. Learners begin by breaking down terms into their prime factors and move on to identifying common factors, and determining the HCF for both pairs and sets of expressions.

As they progress, students apply reasoning skills to explain why the HCF takes the lowest powers of variables and test their understanding with open-ended and matching problems. Later questions introduce factorising using the HCF and reasoning challenges such as “always, sometimes, or never” statements to deepen conceptual understanding.

This worksheet provides an excellent starting point for learning factorisation, giving students the foundational skills they need before moving on to expanding and factorising more complex algebraic expressions.

By the end of this worksheet, students will confidently determine and apply the highest common factors in algebraic contexts, bridging number skills with algebraic manipulation.