What is GCF of 39 and 65?

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GCF of 39 and 65 is 13

How to find GCF of two numbers

Steps to find GCF of 39 and 65

Find all the numbers that would divide 39 and 65 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 39 and 65, and read off the answer!

Example: Find gcf of 39 and 65

Factors for 39: 1, 3, 13, 39
Factors for 65: 1, 5, 13, 65

Hence, GCf of 39 and 65 is 13

How do you explain GCF in mathematics?

GCF or greatest common factor of two or more numbers is defined as largest possible number or integer which is the factor of all given number or in other words we can say that largest possible common number which completely divides the given numbers. GCF of two numbers can be represented as GCF (39, 65).

Properties of GCF

The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
GCF of two consecutive numbers is always 1.
Given two numbers 39 and 65, such that GCF is 13 where 13 will always be less than 39 and 65.
Product of two numbers is always equal to the product of their GCF and LCM.

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of Factors

Every number is a factor of zero (0), since 39 x 0 = 0 and 65 x 0 = 0.
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, 3, 13, 39 are exact divisors of 39 and 1, 5, 13, 65 are exact divisors of 65.
Factors of 39 are 1, 3, 13, 39. Each factor divides 39 without leaving a remainder.
Simlarly, factors of 65 are 1, 5, 13, 65. Each factor divides 65 without leaving a remainder.

Steps to find Factors of 39 and 65

Step 1. Find all the numbers that would divide 39 and 65 without leaving any remainder. Starting with the number 1 upto 19 (half of 39) and 1 upto 32 (half of 65). The number 1 and the number itself are always factors of the given number.

39 ÷ 1 : Remainder = 0

65 ÷ 1 : Remainder = 0

39 ÷ 3 : Remainder = 0

65 ÷ 5 : Remainder = 0

39 ÷ 13 : Remainder = 0

65 ÷ 13 : Remainder = 0

39 ÷ 39 : Remainder = 0

65 ÷ 65 : Remainder = 0

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

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

Examples of GCF

Sammy baked 39 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 39 and 65.
GCF of 39 and 65 is 13.

A class has 39 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 39 and 65. Hence, GCF of 39 and 65 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.

Ram has 39 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 39 and 65. Hence GCF of 39 and 65 is 13. So the number of tables that can be arranged is 13.

Ariel is making ready to eat meals to share with friends. She has 39 bottles of water and 65 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 39 and 65. So the GCF of 39 and 65 is 13.

Mary has 39 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 39 and 65. Hence, the GCF of 39 and 65 or the greatest arrangement is 13.

Kamal is making identical balloon arrangements for a party. He has 39 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 39 and 65. So the GCF of 39 and 65 is 13.

Kunal is making baskets full of nuts and dried fruits. He has 39 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 39 and 65. So the GCF of 39 and 65 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 39 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 39 and 65. Hence, GCF of 39 and 65 is 13.