## FINDING GREATEST COMMON FACTOR

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.

## What is greatest common factor (G.C.F)?

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   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 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

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 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 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 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  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 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 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 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 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 G.C.F  is 10

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