On the webpage, "Greatest common factor with variables and exponents examples" we are going to see how to find HCF or GCF.

To find the greatest 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 greatest 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 greatest common factor is 7 x² y z³**

Let us see the next example on "Greatest common factor with variables and exponents examples".

**Question 2 :**

Find the greatest 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 greatest common factor is x² y**

**Let us see the next example on "Greatest common factor with variables and exponents examples".**

**Question 3 :**

Find the greatest 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 greatest common factor is 5 c³**

**Let us see the next example on "Greatest common factor with variables and exponents examples".**

**Question 4 :**

Find the greatest 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 greatest common factor is **7 x y z²

Let us see the next example on "Greatest common factor with variables and exponents examples".

**Question 5 :**

Find the greatest 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 greatest common factor is **7 m n

Let us see the next example on "Greatest common factor with variables and exponents examples".

Question 6 :

Find the greatest 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 greatest common factor is **6xy

Let us see the next example on "Greatest common factor with variables and exponents examples".

Question 7 :

Find the greatest 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 greatest common factor is 4**

**Let us see the next example on "Greatest common factor with variables and exponents examples".**

Question 8 :

Find the greatest 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 greatest common factor is ****10 ****x²**

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