What is GCF of 115 and 138?

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GCF of 115 and 138 is 23

How to find GCF of two numbers

Steps to find GCF of 115 and 138

Find all the numbers that would divide 115 and 138 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 115 and 138, and read off the answer!

Example: Find gcf of 115 and 138

Factors for 115: 1, 5, 23, 115
Factors for 138: 1, 2, 3, 6, 23, 46, 69, 138

Hence, GCf of 115 and 138 is 23

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 (115, 138).

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 115 and 138, such that GCF is 23 where 23 will always be less than 115 and 138.
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 115 x 0 = 0 and 138 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, 5, 23, 115 are exact divisors of 115 and 1, 2, 3, 6, 23, 46, 69, 138 are exact divisors of 138.
Factors of 115 are 1, 5, 23, 115. Each factor divides 115 without leaving a remainder.
Simlarly, factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138. Each factor divides 138 without leaving a remainder.

Steps to find Factors of 115 and 138

Step 1. Find all the numbers that would divide 115 and 138 without leaving any remainder. Starting with the number 1 upto 57 (half of 115) and 1 upto 69 (half of 138). The number 1 and the number itself are always factors of the given number.

115 ÷ 1 : Remainder = 0

138 ÷ 1 : Remainder = 0

115 ÷ 5 : Remainder = 0

138 ÷ 2 : Remainder = 0

115 ÷ 23 : Remainder = 0

138 ÷ 3 : Remainder = 0

115 ÷ 115 : Remainder = 0

138 ÷ 6 : Remainder = 0

138 ÷ 23 : Remainder = 0

138 ÷ 46 : Remainder = 0

138 ÷ 69 : Remainder = 0

138 ÷ 138 : Remainder = 0

Hence, Factors of 115 are 1, 5, 23, and 115

And, Factors of 138 are 1, 2, 3, 6, 23, 46, 69, and 138

Examples of GCF

Sammy baked 115 chocolate cookies and 138 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 115 and 138.
GCF of 115 and 138 is 23.

A class has 115 boys and 138 girls. A choir teacher wants to form a choir team from this class such that the students are standing in equal rows also girls or boys will be in each row. Teacher wants to know the greatest number of students that could be in each row, can you help him?

To find the greatest number of students that could be in each row, we need to find the GCF of 115 and 138. Hence, GCF of 115 and 138 is 23.

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(115, 138) = ( 115 * 138 ) / LCM(115, 138) = 23.

What is the GCF of 115 and 138?

GCF of 115 and 138 is 23.

Ariel is making ready to eat meals to share with friends. She has 115 bottles of water and 138 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 115 and 138. So the GCF of 115 and 138 is 23.

Mary has 115 blue buttons and 138 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 115 and 138. Hence, the GCF of 115 and 138 or the greatest arrangement is 23.

Kamal is making identical balloon arrangements for a party. He has 115 maroon balloons, and 138 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 115 and 138. So the GCF of 115 and 138 is 23.

Kunal is making baskets full of nuts and dried fruits. He has 115 bags of nuts and 138 bags of dried fruits. He wants each basket to be identical, containing the same combination of bags of nuts and bags of driesn fruits, with no left overs. What is the greatest number of baskets that Kunal can make?

the greatest number of baskets that Kunal can make would be equal to GCF of 115 and 138. So the GCF of 115 and 138 is 23.