What is GCF of 78 and 130?

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GCF of 78 and 130 is 26

How to find GCF of two numbers

Steps to find GCF of 78 and 130

Find all the numbers that would divide 78 and 130 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 78 and 130, and read off the answer!

Example: Find gcf of 78 and 130

Factors for 78: 1, 2, 3, 6, 13, 26, 39, 78
Factors for 130: 1, 2, 5, 10, 13, 26, 65, 130

Hence, GCf of 78 and 130 is 26

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 (78, 130).

Properties of GCF

Given two numbers 78 and 130, such that GCF is 26 where 26 will always be less than 78 and 130.
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. 78 and 130 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, 13, 26, 39, 78 are exact divisors of 78 and 1, 2, 5, 10, 13, 26, 65, 130 are exact divisors of 130.
1 is a factor of every number. Eg. 1 is a factor of 78 and also of 130.
Every number is a factor of zero (0), since 78 x 0 = 0 and 130 x 0 = 0.

Steps to find Factors of 78 and 130

Step 1. Find all the numbers that would divide 78 and 130 without leaving any remainder. Starting with the number 1 upto 39 (half of 78) and 1 upto 65 (half of 130). The number 1 and the number itself are always factors of the given number.

78 ÷ 1 : Remainder = 0

130 ÷ 1 : Remainder = 0

78 ÷ 2 : Remainder = 0

130 ÷ 2 : Remainder = 0

78 ÷ 3 : Remainder = 0

130 ÷ 5 : Remainder = 0

78 ÷ 6 : Remainder = 0

130 ÷ 10 : Remainder = 0

78 ÷ 13 : Remainder = 0

130 ÷ 13 : Remainder = 0

78 ÷ 26 : Remainder = 0

130 ÷ 26 : Remainder = 0

78 ÷ 39 : Remainder = 0

130 ÷ 65 : Remainder = 0

78 ÷ 78 : Remainder = 0

130 ÷ 130 : Remainder = 0

Hence, Factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78

And, Factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130

Examples of GCF

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

GCF and LCM of two numbers can be related as GCF(78, 130) = ( 78 * 130 ) / LCM(78, 130) = 26.

What is the GCF of 78 and 130?

GCF of 78 and 130 is 26.

Ram has 78 cans of Pepsi and 130 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 78 and 130. Hence GCF of 78 and 130 is 26. So the number of tables that can be arranged is 26.

Rubel is creating individual servings of starters for her birthday party. He has 78 pizzas and 130 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 78 and 130. Thus GCF of 78 and 130 is 26.

Ariel is making ready to eat meals to share with friends. She has 78 bottles of water and 130 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 78 and 130. So the GCF of 78 and 130 is 26.

Mary has 78 blue buttons and 130 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 78 and 130. Hence, the GCF of 78 and 130 or the greatest arrangement is 26.

Kamal is making identical balloon arrangements for a party. He has 78 maroon balloons, and 130 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 78 and 130. So the GCF of 78 and 130 is 26.

Kunal is making baskets full of nuts and dried fruits. He has 78 bags of nuts and 130 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 78 and 130. So the GCF of 78 and 130 is 26.

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 78 bus tickets and 130 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 78 and 130. Hence, GCF of 78 and 130 is 26.