What is GCF of 130 and 169?

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GCF of 130 and 169 is 13

How to find GCF of two numbers

Steps to find GCF of 130 and 169

Find all the numbers that would divide 130 and 169 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 130 and 169, and read off the answer!

Example: Find gcf of 130 and 169

Factors for 130: 1, 2, 5, 10, 13, 26, 65, 130
Factors for 169: 1, 13, 169

Hence, GCf of 130 and 169 is 13

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 (130, 169).

Properties of GCF

Given two numbers 130 and 169, such that GCF is 13 where 13 will always be less than 130 and 169.
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 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

Each number is a factor of itself. Eg. 130 and 169 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, 5, 10, 13, 26, 65, 130 are exact divisors of 130 and 1, 13, 169 are exact divisors of 169.
1 is a factor of every number. Eg. 1 is a factor of 130 and also of 169.
Every number is a factor of zero (0), since 130 x 0 = 0 and 169 x 0 = 0.

Steps to find Factors of 130 and 169

Step 1. Find all the numbers that would divide 130 and 169 without leaving any remainder. Starting with the number 1 upto 65 (half of 130) and 1 upto 84 (half of 169). The number 1 and the number itself are always factors of the given number.

130 ÷ 1 : Remainder = 0

169 ÷ 1 : Remainder = 0

130 ÷ 2 : Remainder = 0

169 ÷ 13 : Remainder = 0

130 ÷ 5 : Remainder = 0

169 ÷ 169 : Remainder = 0

130 ÷ 10 : Remainder = 0

130 ÷ 13 : Remainder = 0

130 ÷ 26 : Remainder = 0

130 ÷ 65 : Remainder = 0

130 ÷ 130 : Remainder = 0

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

And, Factors of 169 are 1, 13, and 169

Examples of GCF

Sammy baked 130 chocolate cookies and 169 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 130 and 169.
GCF of 130 and 169 is 13.

A class has 130 boys and 169 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 130 and 169. Hence, GCF of 130 and 169 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(130, 169) = ( 130 * 169 ) / LCM(130, 169) = 13.

What is the GCF of 130 and 169?

GCF of 130 and 169 is 13.

Mary has 130 blue buttons and 169 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 130 and 169. Hence, the GCF of 130 and 169 or the greatest arrangement is 13.

Kamal is making identical balloon arrangements for a party. He has 130 maroon balloons, and 169 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 130 and 169. So the GCF of 130 and 169 is 13.

Kunal is making baskets full of nuts and dried fruits. He has 130 bags of nuts and 169 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 130 and 169. So the GCF of 130 and 169 is 13.

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 130 bus tickets and 169 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 130 and 169. Hence, GCF of 130 and 169 is 13.