GREATEST COMMON FACTOR OF MONOMIALS

About "Greatest common factor of monomials"

How to find greatest common factor of monomials ?

Greatest common factor is the largest common factor of two or more numbers.

To find the greatest common factor of the given numbers (first method) we have to follow the steps given below.

Step 1 :

List the prime factors of each of the given number

Step 2 :

List the common factors of the given numbers.

Step 3 :

Multiply those common factors

Greatest common factor of monomials - Examples

Example 1 :

Find the greatest common factor of

7 x² y z⁴ , 21 x² y⁵ z³

Solution :

7 x² y z⁴  =  7  x²  y  z³  z

21 x² y⁵ z³ = 7 ⋅  x²  y  y⁴

Hence, the greatest common factor is 7 x² y z³

Example 2 :

Find the greatest common factor of

x² y,  x³ y , x² y²

Solution :

x² y  =  x²  y

x³ y  =  x² x  y

x² y²  =  x²   y   y

Hence, the greatest common factor  is  x² y

Example 3 :

Find the greatest common factor of

25 b c⁴ d³ , 35 b² c⁵ , 45 c³ d

Solution :

25 b c⁴ d³  =   5 ⋅  b  c³  d  d  d

35 b² c⁵  =  7 ⋅ 5 ⋅ b ⋅  ⋅ c³ ⋅

45 c³ d  =  3 ⋅ ⋅ 5 ⋅  ⋅ d

Hence, the greatest common factor is 5 c³

Example 4 :

Find the greatest common factor of

35 x⁵ y³ z⁴ , 49 x² y z³ , 14 x y² z²

Solution :

35 x⁵ y³ z⁴  = 7 5 ⋅ ⋅ ⋅ x ⋅ ⋅ x ⋅ ⋅ ⋅ ⋅ ⋅ z²

49 x² y z³  =   7 ⋅ ⋅ x ⋅ ⋅ ⋅ z² ⋅ z

14 x y² z² = 2 ⋅ ⋅ x ⋅ ⋅ ⋅

Hence, the greatest common factor is 7 x y z²

Example 5 :

Find the greatest common factor of the following

x³ y² , x y z

Solution :

x³ y²  =  ⋅ ⋅ x ⋅ ⋅

x y z  =   x ⋅ z

Hence, the greatest common factor is x y.

Example 6 :

Find the greatest common factor of the following

3 x² y z , 4 x³ y³

Solution :

3 x² y z  =  3 ⋅ ⋅  ⋅ ⋅ z

4 x³ y³  =   4 ⋅ x ⋅ x  x ⋅ ⋅ y ⋅ y

Hence, the greatest common factor is x² y.

Example 7 :

Find the greatest common factor of the following

a² b c , b² c a , c² a b

Solution :

a² b c  =  a ⋅ a ⋅ b  c

b² c a   =  b ⋅ b ⋅ c  a

c² a b  =  c ⋅ c ⋅ a  b

Hence, the greatest common factor is abc.

Example 8 :

Find the greatest common factor of the following

66 a⁴ b² c³ , 44 a³ b⁴ c² , 24 a² b³ c⁴

Solution :

66 a⁴ b² c³  =  2 ⋅ 3 ⋅ 11 a⁴  b² c³

44 a³ b⁴ c²  =  2² ⋅ 11 ⋅ a³ ⋅ b⁴  ⋅

24 a² b³ c⁴  =  2³  ⋅ a² ⋅ b³ ⋅  c⁴

=  2 a²b²c²

Hence, the greatest common factor is a²b²c.

After having gone through the stuff given above, we hope that the students would have understood "Greatest common factor of monomials".

Apart from the stuff given above, if you want to know more about "Greatest-common factor of monomials", please click here

Apart from the stuff given in this section, 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

Word problems on quadratic 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