The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Finding the HCF of Algebraic Expressions

In this worksheet, students find the highest common factor of two algebraic expressions.

'Finding the HCF of Algebraic Expressions' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

This worksheet is about finding the Highest Common Factor (HCF) of two algebraic expressions.

 

Example 1

Find the HCF of 3p2qr3 and 6pq3r2

 

Answer


Take each term in turn.


HCF of 3 and 6 is 3.
HCF of p2 and p is p.
HCF of q and q3 is q.
HCF of r3 and r2 is r2.


So, required HCF is 3pqr2.


Example 2

Find the HCF of 4y(y - 7)(7y + 4) and (y - 7)2(7y + 4)

 

Answer


The highest terms common to both are (y - 7) and (7y + 4).

So the HCF is (y - 7)(7y + 4)

Select the correct HCF of these two algebraic expressions

(y-5)(5y+5)2 and (y+5)(5y+5)

(5y+5)

(y-5)

Select the correct HCF of these two algebraic expressions

8p4q3r11 and 5p5q6r4

 

40pqr

p 4 q 3 r 4

Select the correct HCF of these two algebraic expressions

(y-6)(6y+6) 2 and (y+6)(6y+6)

(y+6)(y-6)

(6y+6)

Select the correct HCF of these two algebraic expressions

(y-3)2 (3y+3) and (y-3)3 (3y+3)

 

 

(y-3) 2 (3y+3)

(6y+6)

Select the correct HCF of these two algebraic expressions

p 5 q 6 r 4 and 4p 2 q 3 r 4

p 2qr

p 2 q 3 r 4

Select the correct HCF of these two algebraic expressions

(y-2)(2y+8) 2 and (y+2)(2y+8)

(y-3) 2 (3y+3)

(2y+8)

Select the correct HCF of these two algebraic expressions

4p q 5 r 2 and 6 p q 4

 

4pqr

2p q 4 r

Select the correct HCF of these two algebraic expressions

7p 5 q 4 r  and 21p  q 6 r 6

 

7p q 4 r

14p q 4 r

Select the correct HCF of these two algebraic expressions

2p 6 q 3 r 3 and 4p 2 q 5 r 6

 

8p 1 q 4 r 1

2p 2 q 3 r 3

Select the correct HCF of these two algebraic expressions

(y-4) 2 (4y+7)3 and (y-4) 3 (4y+7)

(y-4)(4y+7)

(y-4) 2 (4y+7)

  • Question 1

Select the correct HCF of these two algebraic expressions

(y-5)(5y+5)2 and (y+5)(5y+5)

CORRECT ANSWER
(5y+5)
EDDIE SAYS
The only expression that appears in both is (5y + 5)
  • Question 2

Select the correct HCF of these two algebraic expressions

8p4q3r11 and 5p5q6r4

 

CORRECT ANSWER
p 4 q 3 r 4
EDDIE SAYS

In each expression we have p4, q3 and r4

  • Question 3

Select the correct HCF of these two algebraic expressions

(y-6)(6y+6) 2 and (y+6)(6y+6)

CORRECT ANSWER
(6y+6)
EDDIE SAYS
The only term that appears in both expressions is (6y + 6)
  • Question 4

Select the correct HCF of these two algebraic expressions

(y-3)2 (3y+3) and (y-3)3 (3y+3)

 

 

CORRECT ANSWER
(y-3) 2 (3y+3)
EDDIE SAYS
In both expressions we have (3y + 3) and at least two lots of (y - 3)
  • Question 5

Select the correct HCF of these two algebraic expressions

p 5 q 6 r 4 and 4p 2 q 3 r 4

CORRECT ANSWER
p 2 q 3 r 4
EDDIE SAYS

In both expressions we have p2, q3 and r4

  • Question 6

Select the correct HCF of these two algebraic expressions

(y-2)(2y+8) 2 and (y+2)(2y+8)

CORRECT ANSWER
(2y+8)
EDDIE SAYS
The only term that appears in both expressions is (2y + 8)
  • Question 7

Select the correct HCF of these two algebraic expressions

4p q 5 r 2 and 6 p q 4

 

CORRECT ANSWER
2p q 4 r
EDDIE SAYS

In both expressions we have the number 2, p, q4 and r

  • Question 8

Select the correct HCF of these two algebraic expressions

7p 5 q 4 r  and 21p  q 6 r 6

 

CORRECT ANSWER
7p q 4 r
EDDIE SAYS

In both expressions we have a factor of 7 and factors of p, q5 and r

  • Question 9

Select the correct HCF of these two algebraic expressions

2p 6 q 3 r 3 and 4p 2 q 5 r 6

 

CORRECT ANSWER
2p 2 q 3 r 3
EDDIE SAYS

In both expressions we have factors of 2, p2, q3 and r3

  • Question 10

Select the correct HCF of these two algebraic expressions

(y-4) 2 (4y+7)3 and (y-4) 3 (4y+7)

CORRECT ANSWER
(y-4) 2 (4y+7)
EDDIE SAYS
There are a number of factors here, (y - 4) appears at least twice in both expressions (4y + 7) appears at least once in both expressions
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.