What is GCF of 6 and 21?

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GCF of 6 and 21 is 3

How to find GCF of two numbers

Steps to find GCF of 6 and 21

Find all the numbers that would divide 6 and 21 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 6 and 21, and read off the answer!

Example: Find gcf of 6 and 21

Factors for 6: 1, 2, 3, 6
Factors for 21: 1, 3, 7, 21

Hence, GCf of 6 and 21 is 3

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 (6, 21).

Properties of GCF

Given two numbers 6 and 21, such that GCF is 3 where 3 will always be less than 6 and 21.
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. 6 and 21 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, 3, 6 are exact divisors of 6 and 1, 3, 7, 21 are exact divisors of 21.
1 is a factor of every number. Eg. 1 is a factor of 6 and also of 21.
Every number is a factor of zero (0), since 6 x 0 = 0 and 21 x 0 = 0.

Steps to find Factors of 6 and 21

Step 1. Find all the numbers that would divide 6 and 21 without leaving any remainder. Starting with the number 1 upto 3 (half of 6) and 1 upto 10 (half of 21). The number 1 and the number itself are always factors of the given number.

6 ÷ 1 : Remainder = 0

21 ÷ 1 : Remainder = 0

6 ÷ 2 : Remainder = 0

21 ÷ 3 : Remainder = 0

6 ÷ 3 : Remainder = 0

21 ÷ 7 : Remainder = 0

6 ÷ 6 : Remainder = 0

21 ÷ 21 : Remainder = 0

Hence, Factors of 6 are 1, 2, 3, and 6

And, Factors of 21 are 1, 3, 7, and 21

Examples of GCF

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

GCF and LCM of two numbers can be related as GCF(6, 21) = ( 6 * 21 ) / LCM(6, 21) = 3.

What is the GCF of 6 and 21?

GCF of 6 and 21 is 3.

Ram has 6 cans of Pepsi and 21 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 6 and 21. Hence GCF of 6 and 21 is 3. So the number of tables that can be arranged is 3.

Rubel is creating individual servings of starters for her birthday party. He has 6 pizzas and 21 hamburgers. He wants each serving to be identical, with no left overs. Can you help Rubel in arranging the same in greatest possible way?

The greatest number of servings Rubel can create would be equal to the GCF of 6 and 21. Thus GCF of 6 and 21 is 3.

Ariel is making ready to eat meals to share with friends. She has 6 bottles of water and 21 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 6 and 21. So the GCF of 6 and 21 is 3.

Mary has 6 blue buttons and 21 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 6 and 21. Hence, the GCF of 6 and 21 or the greatest arrangement is 3.

Kamal is making identical balloon arrangements for a party. He has 6 maroon balloons, and 21 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 6 and 21. So the GCF of 6 and 21 is 3.

Kunal is making baskets full of nuts and dried fruits. He has 6 bags of nuts and 21 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 6 and 21. So the GCF of 6 and 21 is 3.

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 6 bus tickets and 21 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 6 and 21. Hence, GCF of 6 and 21 is 3.