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

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 **x ** z³ **x ** z

Prime factors of 7 x² y z⁴ = 7 **x **3 **x **x² **x** y **x** y⁴ **x **z³

**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 **y

Prime factors of x³ y = x² **x** x **x **y

Prime factors of x² y² = x² **x** ** **y **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 = 7 **x** 5 **x** x **x** x⁴** ****x **** **y² **x **y **x **z² **x** z²

Prime factors of

49 x² y z³ = 7 **x** 7 **x** x** x** x **x**** **y **x**** **z² **x** z

Prime factors of 14 x y² z² = 2 **x** 7 **x** x **x**** **y x y **x**** **z²

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 = 7 **x** 5 **x** n **x** n** ****x **** m**

Prime factors of 21 m² n = 7 **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 **x** 2 x 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 **x** 5 **x** 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**

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