## HIGHEST COMMON FACTOR WITH VARIABLES WORKSHEET

On the webpage, "Highest common factor with variables worksheet" we are going to see some practice questions.

(1) Find the highest common factor of 7 x²yz⁴ , 21x²y⁵z³

(2) Find the highest common factor of x²y,  x³y , x²y²

(3) Find the highest common factor of 25 b c⁴ d³ , 35 b² c⁵ , 45 c³ d

(4) Find the highest common factor of 35 x⁵ y³ z⁴ , 49 x² y z³ , 14 x y² z²

(5) Find the highest common factor of 35 n²m, 21 m² n

(6) Find the highest common factor of 66 y x, 30 x² y

(7) Find the highest common factor of 60 y, 56 x²

(8) Find the highest common factor of 80 x³, 30 x²y

## Highest common factor with variables worksheet - answers

To find the highest common factor of the given numbers or for algebraic expressions we have to follow the steps:

Step 1: List the prime factors of each of the given number. For algebraic expression we have to find factors of them.

Step 2: List the common factors of the given numbers or common factors.

Step 3: Multiply those common factors.

Question 1 :

Find the highest common factor of 7 x² y z⁴ , 21 x²y⁵ z³

Solution :

Step 1 :

Prime factors of  7 x² y z⁴  =  7 x  x² x  y   z

Prime factors of  7 x² y z⁴  =  7  3 x x  y x y⁴ x

Step 2 : Common factors that we find in both terms are 7,x², y  and z³

Step 3 :

Multiply the common factors  7,x², y  and z³

Hence, the highest common factor is 7 x² y z³

Let us see the next example on "Highest common factor with variables worksheet".

Question 2 :

Find the highest common factor of x² y,  x³ y , x² y²

Solution:

Step 1 :

Prime factors of x² y =  x² x

Prime factors of x³ y =  x² x  x x

Prime factors of x² y² =  x² x   x   y

Step 2 : The common factors that we find from given terms are x² and y

Step 3 :

Multiply the common factors  x² and y

Hence, the highest common factor is x² y

Let us see the next example on "Highest common factor with variables worksheet".

Question 3 :

Find the highest common factor of 25 b c⁴ d³ , 35 b² c⁵ , 45 c³ d

Solution:

Step 1 :

Prime factors of 25 b c⁴ d³ = 5 x 5 x b x c³ x d x d x d

Prime factors of 35 b² c⁵ = 7 x 5 x b x b x c³ x c²

Prime factors of 45 c³ d  = 3 x 3 x 5 x c³ x d

Step 2 : The common factors that we find from given terms are 5 and c³

Step 3 :

Multiply the common factors  5 and c³

Hence, the highest common factor is 5 c³

Let us see the next example on "Highest common factor with variables worksheet".

Question 4 :

Find the highest common factor of 35 x⁵ y³ z⁴ , 49 x² y z³ , 14 x y² z²

Solution:

Step 1 :

Prime factors of

35 x⁵ Y³z⁴ x 5 x x x x  y² x  x  z² x z²

Prime factors of

49 x² y z³  x 7 x x x x x  x  z² x z

Prime factors of 14 x y² z² x 7 x x x  y xx The common factors that we find from given terms are 7, x, y and z²

Step 3 :

Multiply the common factors  7, x, y and z²

Hence, the highest common factor is 7 x y z²

Let us see the next example on "Highest common factor with variables worksheet".

Question 5 :

Find the highest common factor of 35 n²m, 21 m² n

Solution:

Step 1 :

Prime factors of 35 n²m  x 5 x n x n  m

Prime factors of 21 m² n   x 3 x m x m x  n

Step 2 :

The common factors are 7, m and n

Step 3 :

Multiply the common factors  7, m and n

Hence, the highest common factor is 7 m n

Let us see the next example on "Highest common factor with variables worksheet".

Question 6 :

Find the highest common factor of 66 y x, 30 x² y

Solution:

Step 1 :

Prime factors of 66 y x  = 2 x 3 x 11 x y x x

Prime factors of 30 x² y = 3 x 2 x 5 x x x  x  x y

Step 2 :

The common factors are 2, 3, x and y

Step 3 :

Multiply the common factors  2, 3, x and y

Hence, the highest common factor is 6xy

Let us see the next example on "Highest common factor with variables worksheet".

Question 7 :

Find the highest common factor of 60 y, 56 x²

Solution:

Step 1 :

Prime factors of 60 y  =  2 xx 3 x 5 x y

Prime factors of 56 x²  =  2 x 2 x 2 x 7 x  x  x x

Step 2 :

The common factors are 2 and 2

Step 3 :

Multiply the common factors  2 and 2

Hence, the highest common factor is 4

Let us see the next example on "Highest common factor with variables worksheet".

Question 8 :

Find the highest common factor of 80 x³, 30 x²y

Solution:

Step 1 :

Prime factors of 80 x³  =  2 x 2 x 2 x 2 xx x² x x

Prime factors of 30 x²y   =  2 x 3 x 5 x x² x  y

Step 2 :

The common factors are 2, 5 and x²

Step 3 :

Multiply the common factors  2, 5 and x²

Hence, the highest common factor is 10 x²

After having gone through the stuff given above, we hope that the students would have understood "Highest common factor with variables worksheet".

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