What is GCF of 8 and 22?

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GCF of 8 and 22 is 2

How to find GCF of two numbers

Steps to find GCF of 8 and 22

Find all the numbers that would divide 8 and 22 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 8 and 22, and read off the answer!

Example: Find gcf of 8 and 22

Factors for 8: 1, 2, 4, 8
Factors for 22: 1, 2, 11, 22

Hence, GCf of 8 and 22 is 2

What does GCF mean in mathematics?

Greatest Common Fcator (GCF) or also sometimes written as greates common divisor is the largest number that can evenly divide the given two numbers. GCF is represented as GCF (8, 22).

Properties of GCF

The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 8 and 22 is 2, where 2 is less than both 8 and 22.
GCF of two consecutive numbers is always 1.
The product of GCF and LCM of two given numbers is equal to the product of two numbers.
The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of Factors

Each number is a factor of itself. Eg. 8 and 22 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 8 and also of 22.
Every number is a factor of zero (0), since 8 x 0 = 0 and 22 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, 2, 4, 8 are exact divisors of 8 and 1, 2, 11, 22 are exact divisors of 22.
Factors of 8 are 1, 2, 4, 8. Each factor divides 8 without leaving a remainder.
Simlarly, factors of 22 are 1, 2, 11, 22. Each factor divides 22 without leaving a remainder.
Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8 are all less than or equal to 8 and 1, 2, 11, 22 are all less than or equal to 22.

Steps to find Factors of 8 and 22

Step 1. Find all the numbers that would divide 8 and 22 without leaving any remainder. Starting with the number 1 upto 4 (half of 8) and 1 upto 11 (half of 22). The number 1 and the number itself are always factors of the given number.

8 ÷ 1 : Remainder = 0

22 ÷ 1 : Remainder = 0

8 ÷ 2 : Remainder = 0

22 ÷ 2 : Remainder = 0

8 ÷ 4 : Remainder = 0

22 ÷ 11 : Remainder = 0

8 ÷ 8 : Remainder = 0

22 ÷ 22 : Remainder = 0

Hence, Factors of 8 are 1, 2, 4, and 8

And, Factors of 22 are 1, 2, 11, and 22

Examples of GCF

Sammy baked 8 chocolate cookies and 22 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 8 and 22.
GCF of 8 and 22 is 2.

A class has 8 boys and 22 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 8 and 22. Hence, GCF of 8 and 22 is 2.

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(8, 22) = ( 8 * 22 ) / LCM(8, 22) = 2.

What is the GCF of 8 and 22?

GCF of 8 and 22 is 2.

Ariel is making ready to eat meals to share with friends. She has 8 bottles of water and 22 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 8 and 22. So the GCF of 8 and 22 is 2.

Mary has 8 blue buttons and 22 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 8 and 22. Hence, the GCF of 8 and 22 or the greatest arrangement is 2.

Kamal is making identical balloon arrangements for a party. He has 8 maroon balloons, and 22 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 8 and 22. So the GCF of 8 and 22 is 2.

Kunal is making baskets full of nuts and dried fruits. He has 8 bags of nuts and 22 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 8 and 22. So the GCF of 8 and 22 is 2.