What is GCF of 138 and 345?

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GCF of 138 and 345 is 69

How to find GCF of two numbers

Steps to find GCF of 138 and 345

Find all the numbers that would divide 138 and 345 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 138 and 345, and read off the answer!

Example: Find gcf of 138 and 345

Factors for 138: 1, 2, 3, 6, 23, 46, 69, 138
Factors for 345: 1, 3, 5, 15, 23, 69, 115, 345

Hence, GCf of 138 and 345 is 69

What does GCF mean in mathematics?

Greatest Common Fcator (GCF) or also sometimes written as greates common divisor is the largest number that can evenly divide the given two numbers. GCF is represented as GCF (138, 345).

Properties of GCF

Given two numbers 138 and 345, such that GCF is 69 where 69 will always be less than 138 and 345.
GCF of two numbers is always equal to 1 in case given numbers are consecutive.
The product of GCF and LCM of two given numbers is equal to the product of two numbers.
The GCF of two given numbers is either 1 or the number itself if one of them is a prime number.

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of Factors

Each number is a factor of itself. Eg. 138 and 345 are factors of themselves respectively.
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, 2, 3, 6, 23, 46, 69, 138 are exact divisors of 138 and 1, 3, 5, 15, 23, 69, 115, 345 are exact divisors of 345.
1 is a factor of every number. Eg. 1 is a factor of 138 and also of 345.
Every number is a factor of zero (0), since 138 x 0 = 0 and 345 x 0 = 0.

Steps to find Factors of 138 and 345

Step 1. Find all the numbers that would divide 138 and 345 without leaving any remainder. Starting with the number 1 upto 69 (half of 138) and 1 upto 172 (half of 345). The number 1 and the number itself are always factors of the given number.

138 ÷ 1 : Remainder = 0

345 ÷ 1 : Remainder = 0

138 ÷ 2 : Remainder = 0

345 ÷ 3 : Remainder = 0

138 ÷ 3 : Remainder = 0

345 ÷ 5 : Remainder = 0

138 ÷ 6 : Remainder = 0

345 ÷ 15 : Remainder = 0

138 ÷ 23 : Remainder = 0

345 ÷ 23 : Remainder = 0

138 ÷ 46 : Remainder = 0

345 ÷ 69 : Remainder = 0

138 ÷ 69 : Remainder = 0

345 ÷ 115 : Remainder = 0

138 ÷ 138 : Remainder = 0

345 ÷ 345 : Remainder = 0

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

And, Factors of 345 are 1, 3, 5, 15, 23, 69, 115, and 345

Examples of GCF

Sammy baked 138 chocolate cookies and 345 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 138 and 345.
GCF of 138 and 345 is 69.

A class has 138 boys and 345 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 138 and 345. Hence, GCF of 138 and 345 is 69.

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.

Ram has 138 cans of Pepsi and 345 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 138 and 345. Hence GCF of 138 and 345 is 69. So the number of tables that can be arranged is 69.

Ariel is making ready to eat meals to share with friends. She has 138 bottles of water and 345 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 138 and 345. So the GCF of 138 and 345 is 69.

Mary has 138 blue buttons and 345 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 138 and 345. Hence, the GCF of 138 and 345 or the greatest arrangement is 69.

Kamal is making identical balloon arrangements for a party. He has 138 maroon balloons, and 345 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 138 and 345. So the GCF of 138 and 345 is 69.

Kunal is making baskets full of nuts and dried fruits. He has 138 bags of nuts and 345 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 138 and 345. So the GCF of 138 and 345 is 69.

To energize public transportation, Abir needs to give a few companions envelopes with transport tickets, and metro tickets in them. On the off chance that he has 138 bus tickets and 345 metro tickets to be parted similarly among the envelopes, and he need no tickets left. What is the greatest number of envelopes Abir can make?

To make the greatest number of envelopes Abir needs to find out the GCF of 138 and 345. Hence, GCF of 138 and 345 is 69.