**Finding greatest common factor :**

On the webpage, "Greatest common factor" we are going to see how to find HCF or GCF.

We have two methods of finding greatest common factor of given numbers.

**Common divisor method :**

Step 1 :

Find the divisor of given numbers.

Step 2 :

Circle and write the common factors

Step 3 :

Among the common factors the greatest factor is G.C.F or G.C.D

**Factorization method :**

Step 1 :

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

Step 2 :

List the common factors of the given numbers or common factors.

Step 3 :

Multiply those common factors.

Let us see some example problems of finding greatest common factor.

**Question 1 :**

Find the greatest common factor of 30, 42

**Solution :**

**Method 1:(Common divisor method)**

**Step 1 :**

Divisors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

Divisors of 42 = 1, 2, 3, 6, 7, 21, 42

**Step 2 :**

**Step 3 :**

Greatest factor among them is 6.

Hence GCF of 30 and 42 is 6

**Method 2 :(Prime factorization method)**

**Step 1 :**

Prime factors of 30 = 2 x 3 x 5

Prime factors of 42 = 2 x 3 x 7

**Step 2 :**

Circle the common factors

**Step 3 :**

Multiplying the common factors, we get 2 x 3 = 6.

Hence G.C.F of 30 and 42 is 6

Let us see the question on "Finding greatest common factor".

**Question 2 :**

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 G.C.F is 7 x² y z³

Let us see the question on "Finding greatest common factor".

**Question 3 :**

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 G.C.F is x² y

**Question 4 :**

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 G.C.F is 5 c³

**Question 5 :**

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 G.C.F is 7 x y z²

**Question 6 :**

Find G.C.F 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 G.C.F is 7 m n

**Question 7 :**

Find G.C.F 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 G.C.F is 6xy

**Question 8 :**

Find G.C.F 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 G.C.F is 4

**Question 9 :**

Find G.C.F 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 G.C.F is 10 x²

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