What is GCF of 135 and 189?

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GCF of 135 and 189 is 27

How to find GCF of two numbers

Steps to find GCF of 135 and 189

Find all the numbers that would divide 135 and 189 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 135 and 189, and read off the answer!

Example: Find gcf of 135 and 189

Factors for 135: 1, 3, 5, 9, 15, 27, 45, 135
Factors for 189: 1, 3, 7, 9, 21, 27, 63, 189

Hence, GCf of 135 and 189 is 27

Definition of GCF

Greatest common factor commonly known as GCF of the two numbers is the highest possible number which completely divides given numbers, i.e. without leaving any remainder. It is represented as GCF (135, 189).

Properties of GCF

The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
GCF of two consecutive numbers is always 1.
Given two numbers 135 and 189, such that GCF is 27 where 27 will always be less than 135 and 189.
Product of two numbers is always equal to the product of their GCF and LCM.

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of Factors

Every number is a factor of zero (0), since 135 x 0 = 0 and 189 x 0 = 0.
Every number other than 1 has at least two factors, namely the number itself and 1.
Every factor of a number is an exact divisor of that number, example 1, 3, 5, 9, 15, 27, 45, 135 are exact divisors of 135 and 1, 3, 7, 9, 21, 27, 63, 189 are exact divisors of 189.
Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135. Each factor divides 135 without leaving a remainder.
Simlarly, factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189. Each factor divides 189 without leaving a remainder.

Steps to find Factors of 135 and 189

Step 1. Find all the numbers that would divide 135 and 189 without leaving any remainder. Starting with the number 1 upto 67 (half of 135) and 1 upto 94 (half of 189). The number 1 and the number itself are always factors of the given number.

135 ÷ 1 : Remainder = 0

189 ÷ 1 : Remainder = 0

135 ÷ 3 : Remainder = 0

189 ÷ 3 : Remainder = 0

135 ÷ 5 : Remainder = 0

189 ÷ 7 : Remainder = 0

135 ÷ 9 : Remainder = 0

189 ÷ 9 : Remainder = 0

135 ÷ 15 : Remainder = 0

189 ÷ 21 : Remainder = 0

135 ÷ 27 : Remainder = 0

189 ÷ 27 : Remainder = 0

135 ÷ 45 : Remainder = 0

189 ÷ 63 : Remainder = 0

135 ÷ 135 : Remainder = 0

189 ÷ 189 : Remainder = 0

Hence, Factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135

And, Factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189

Examples of GCF

Sammy baked 135 chocolate cookies and 189 fruit and nut cookies to package in plastic containers for her friends at college. She wants to divide the cookies into identical boxes so that each box has the same number of each kind of cookies. She wishes that each box should have greatest number of cookies possible, how many plastic boxes does she need?

Since Sammy wants to pack greatest number of cookies possible. So for calculating total number of boxes required we need to calculate the GCF of 135 and 189.
GCF of 135 and 189 is 27.

What is the difference between GCF and LCM?

Major and simple difference betwen GCF and LCM is that GCF gives you the greatest common factor while LCM finds out the least common factor possible for the given numbers.

What is the relation between LCM and GCF (Greatest Common Factor)?

GCF and LCM of two numbers can be related as GCF(135, 189) = ( 135 * 189 ) / LCM(135, 189) = 27.

What is the GCF of 135 and 189?

GCF of 135 and 189 is 27.

Ram has 135 cans of Pepsi and 189 cans of Coca Cola. He wants to create identical refreshment tables that will be organized in his house warming party. He also doesn't want to have any can left over. What is the greatest number of tables that Ram can arrange?

To find the greatest number of tables that Ram can stock we need to find the GCF of 135 and 189. Hence GCF of 135 and 189 is 27. So the number of tables that can be arranged is 27.

Rubel is creating individual servings of starters for her birthday party. He has 135 pizzas and 189 hamburgers. He wants each serving to be identical, with no left overs. Can you help Rubel in arranging the same in greatest possible way?

The greatest number of servings Rubel can create would be equal to the GCF of 135 and 189. Thus GCF of 135 and 189 is 27.

Ariel is making ready to eat meals to share with friends. She has 135 bottles of water and 189 cans of food, which she would like to distribute equally, with no left overs. What is the greatest number of boxes Ariel can make?

The greatest number of boxes Ariel can make would be equal to GCF of 135 and 189. So the GCF of 135 and 189 is 27.

Mary has 135 blue buttons and 189 white buttons. She wants to place them in identical groups without any buttons left, in the greatest way possible. Can you help Mary arranging them in groups?

Greatest possible way in which Mary can arrange them in groups would be GCF of 135 and 189. Hence, the GCF of 135 and 189 or the greatest arrangement is 27.

Kamal is making identical balloon arrangements for a party. He has 135 maroon balloons, and 189 orange balloons. He wants each arrangement tohave the same number of each color. What is the greatest number of arrangements that he can make if every balloon is used?

The greatest number of arrangements that he can make if every balloon is used would be equal to GCF of 135 and 189. So the GCF of 135 and 189 is 27.