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HCF of algebraic expressions

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HCF of algebraic expressions woksheet
HCF of algebraic expressions woksheet

Finding the Highest Common Factor (HCF) of algebraic expressions is like figuring out what’s shared between different algebraic ‘families.’ Whether you’re simplifying fractions or solving equations, knowing the HCF helps you break down tricky expressions into neat, manageable parts — a bit like finding the biggest piece that fits perfectly into every puzzle! Jump to the questions

Practise now

Topic guide

What this worksheet practises

This worksheet provides practice on finding the Highest Common Factor (HCF) of two or more algebraic terms. This is the exact skill you need to master before you can successfully factorise algebraic expressions into single brackets.

Key method

Finding the HCF of algebraic terms requires looking at the numbers and the letters separately.

  • The Numbers: Look at the coefficients (the big numbers at the front). Find the largest whole number that divides exactly into all of them.
  • The Letters: Look at the variables (the letters). Find the letters that appear in every single term.
  • For those common letters, identify the lowest power that appears.
  • Multiply your number factor and your letter factors together to create the final HCF.

Worked example

Find the Highest Common Factor of 12x³y² and 18x²y&sup4;.

Step 1: Look at the numbers (12 and 18).

The largest number that goes into both 12 and 18 is 6.

Step 2: Look at the 'x' terms (x³ and x²).

The lowest power is x². This is the largest amount of 'x' we can pull out of both terms.

Step 3: Look at the 'y' terms (y² and y&sup4;).

The lowest power is y². This is the largest amount of 'y' we can pull out of both terms.

Step 4: Combine them all together.

The Highest Common Factor is 6x²y².

Common mistakes to avoid

A frequent mistake is picking the highest power of the letters instead of the lowest. For example, looking at x² and x&sup5; and saying the HCF includes x&sup5;. This is impossible, because you cannot pull five 'x's out of a term that only has two. You must always choose the lowest power available.

Things to remember

If the terms don't share any letters (e.g. 4x and 8y), then the HCF will just be a number (4). If the terms don't share any common numbers other than 1 (e.g. 5x² and 7x), the HCF will just be a letter (x).