## GREATEST COMMON FACTOR WITH VARIABLES AND EXPONENTS EXAMPLES

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   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 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

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 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 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 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  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 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 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 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 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 greatest common factor is 10 x²

After having gone through the stuff given above, we hope that the students would have understood "Greatest common factor with variables and exponents examples".

Apart from the stuff given above, if you want to know more about "greatest common factor with variables and exponents examples", please click here

Apart from the stuff, "Greatest common factor with variables and exponents examples", if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6