What is GCF of 117 and 130?

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GCF of 117 and 130 is 13

How to find GCF of two numbers

Steps to find GCF of 117 and 130

Find all the numbers that would divide 117 and 130 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 117 and 130, and read off the answer!

Example: Find gcf of 117 and 130

Factors for 117: 1, 3, 9, 13, 39, 117
Factors for 130: 1, 2, 5, 10, 13, 26, 65, 130

Hence, GCf of 117 and 130 is 13

How do we define GCF?

In mathematics we use GCF or greatest common method to find out the greatest possible positive integer which can completely divide the given numbers. It is written as GCF (117, 130).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 117 and 130 is 13, where 13 is less than both the numbers.
If the given numbers are consecutive than GCF is always 1.
Product of two numbers is always equal to the product of their GCF and LCM.
The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.

How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

Properties of Factors

Every factor of a number is an exact divisor of that number, example 1, 3, 9, 13, 39, 117 are exact divisors of 117 and 1, 2, 5, 10, 13, 26, 65, 130 are exact divisors of 130.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 117 and 130 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 117 and also of 130.

Steps to find Factors of 117 and 130

Step 1. Find all the numbers that would divide 117 and 130 without leaving any remainder. Starting with the number 1 upto 58 (half of 117) and 1 upto 65 (half of 130). The number 1 and the number itself are always factors of the given number.

117 ÷ 1 : Remainder = 0

130 ÷ 1 : Remainder = 0

117 ÷ 3 : Remainder = 0

130 ÷ 2 : Remainder = 0

117 ÷ 9 : Remainder = 0

130 ÷ 5 : Remainder = 0

117 ÷ 13 : Remainder = 0

130 ÷ 10 : Remainder = 0

117 ÷ 39 : Remainder = 0

130 ÷ 13 : Remainder = 0

117 ÷ 117 : Remainder = 0

130 ÷ 26 : Remainder = 0

130 ÷ 65 : Remainder = 0

130 ÷ 130 : Remainder = 0

Hence, Factors of 117 are 1, 3, 9, 13, 39, and 117

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

Examples of GCF

Sammy baked 117 chocolate cookies and 130 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 117 and 130.
GCF of 117 and 130 is 13.

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(117, 130) = ( 117 * 130 ) / LCM(117, 130) = 13.

What is the GCF of 117 and 130?

GCF of 117 and 130 is 13.

Ram has 117 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 117 and 130. Hence GCF of 117 and 130 is 13. So the number of tables that can be arranged is 13.

Rubel is creating individual servings of starters for her birthday party. He has 117 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 117 and 130. Thus GCF of 117 and 130 is 13.

Ariel is making ready to eat meals to share with friends. She has 117 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 117 and 130. So the GCF of 117 and 130 is 13.

Mary has 117 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 117 and 130. Hence, the GCF of 117 and 130 or the greatest arrangement is 13.

Kamal is making identical balloon arrangements for a party. He has 117 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 117 and 130. So the GCF of 117 and 130 is 13.