What is GCF of 10 and 65?

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GCF of 10 and 65 is 5

How to find GCF of two numbers

Steps to find GCF of 10 and 65

Find all the numbers that would divide 10 and 65 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 10 and 65, and read off the answer!

Example: Find gcf of 10 and 65

Factors for 10: 1, 2, 5, 10
Factors for 65: 1, 5, 13, 65

Hence, GCf of 10 and 65 is 5

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 (10, 65).

Properties of GCF

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

Steps to find Factors of 10 and 65

Step 1. Find all the numbers that would divide 10 and 65 without leaving any remainder. Starting with the number 1 upto 5 (half of 10) and 1 upto 32 (half of 65). The number 1 and the number itself are always factors of the given number.

10 ÷ 1 : Remainder = 0

65 ÷ 1 : Remainder = 0

10 ÷ 2 : Remainder = 0

65 ÷ 5 : Remainder = 0

10 ÷ 5 : Remainder = 0

65 ÷ 13 : Remainder = 0

10 ÷ 10 : Remainder = 0

65 ÷ 65 : Remainder = 0

Hence, Factors of 10 are 1, 2, 5, and 10

And, Factors of 65 are 1, 5, 13, and 65

Examples of GCF

Sammy baked 10 chocolate cookies and 65 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 10 and 65.
GCF of 10 and 65 is 5.

A class has 10 boys and 65 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 10 and 65. Hence, GCF of 10 and 65 is 5.

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

GCF and LCM of two numbers can be related as GCF(10, 65) = ( 10 * 65 ) / LCM(10, 65) = 5.

What is the GCF of 10 and 65?

GCF of 10 and 65 is 5.

Ram has 10 cans of Pepsi and 65 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 10 and 65. Hence GCF of 10 and 65 is 5. So the number of tables that can be arranged is 5.

Mary has 10 blue buttons and 65 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 10 and 65. Hence, the GCF of 10 and 65 or the greatest arrangement is 5.

Kamal is making identical balloon arrangements for a party. He has 10 maroon balloons, and 65 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 10 and 65. So the GCF of 10 and 65 is 5.

Kunal is making baskets full of nuts and dried fruits. He has 10 bags of nuts and 65 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 10 and 65. So the GCF of 10 and 65 is 5.

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 10 bus tickets and 65 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 10 and 65. Hence, GCF of 10 and 65 is 5.