What is GCF of 46 and 64?

Go back to 'All gcf of pages' >

GCF of 46 and 64 is 2

How to find GCF of two numbers

Steps to find GCF of 46 and 64

Find all the numbers that would divide 46 and 64 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 46 and 64, and read off the answer!

Example: Find gcf of 46 and 64

Factors for 46: 1, 2, 23, 46
Factors for 64: 1, 2, 4, 8, 16, 32, 64

Hence, GCf of 46 and 64 is 2

What is GCF of two numbers?

In mathematics GCF or also known as greatest common factor of two or more number is that one largest number which is a factor of those given numbers. It is represented as GCF (46, 64).

Properties of GCF

Given two numbers 46 and 64, such that GCF is 2 where 2 will always be less than 46 and 64.
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.

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of Factors

Each number is a factor of itself. Eg. 46 and 64 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, 23, 46 are exact divisors of 46 and 1, 2, 4, 8, 16, 32, 64 are exact divisors of 64.
1 is a factor of every number. Eg. 1 is a factor of 46 and also of 64.
Every number is a factor of zero (0), since 46 x 0 = 0 and 64 x 0 = 0.

Steps to find Factors of 46 and 64

Step 1. Find all the numbers that would divide 46 and 64 without leaving any remainder. Starting with the number 1 upto 23 (half of 46) and 1 upto 32 (half of 64). The number 1 and the number itself are always factors of the given number.

46 ÷ 1 : Remainder = 0

64 ÷ 1 : Remainder = 0

46 ÷ 2 : Remainder = 0

64 ÷ 2 : Remainder = 0

46 ÷ 23 : Remainder = 0

64 ÷ 4 : Remainder = 0

46 ÷ 46 : Remainder = 0

64 ÷ 8 : Remainder = 0

64 ÷ 16 : Remainder = 0

64 ÷ 32 : Remainder = 0

64 ÷ 64 : Remainder = 0

Hence, Factors of 46 are 1, 2, 23, and 46

And, Factors of 64 are 1, 2, 4, 8, 16, 32, and 64

Examples of GCF

Sammy baked 46 chocolate cookies and 64 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 46 and 64.
GCF of 46 and 64 is 2.

A class has 46 boys and 64 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 46 and 64. Hence, GCF of 46 and 64 is 2.

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

GCF and LCM of two numbers can be related as GCF(46, 64) = ( 46 * 64 ) / LCM(46, 64) = 2.

What is the GCF of 46 and 64?

GCF of 46 and 64 is 2.

Ram has 46 cans of Pepsi and 64 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 46 and 64. Hence GCF of 46 and 64 is 2. So the number of tables that can be arranged is 2.

Mary has 46 blue buttons and 64 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 46 and 64. Hence, the GCF of 46 and 64 or the greatest arrangement is 2.

Kamal is making identical balloon arrangements for a party. He has 46 maroon balloons, and 64 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 46 and 64. So the GCF of 46 and 64 is 2.

Kunal is making baskets full of nuts and dried fruits. He has 46 bags of nuts and 64 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 46 and 64. So the GCF of 46 and 64 is 2.

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 46 bus tickets and 64 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 46 and 64. Hence, GCF of 46 and 64 is 2.