What is GCF of 7 and 21?

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GCF of 7 and 21 is 7

How to find GCF of two numbers

Steps to find GCF of 7 and 21

Find all the numbers that would divide 7 and 21 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 7 and 21, and read off the answer!

Example: Find gcf of 7 and 21

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

Hence, GCf of 7 and 21 is 7

How do we define GCF?

In mathematics we use GCF or greatest common method to find out the greatest possible positive integer which can completely divide the given numbers. It is written as GCF (7, 21).

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 7 and 21, such that GCF is 7 where 7 will always be less than 7 and 21.
Product of two numbers is always equal to the product of their GCF and LCM.

How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

Properties of Factors

Every number is a factor of zero (0), since 7 x 0 = 0 and 21 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, 7 are exact divisors of 7 and 1, 3, 7, 21 are exact divisors of 21.
Factors of 7 are 1, 7. Each factor divides 7 without leaving a remainder.
Simlarly, factors of 21 are 1, 3, 7, 21. Each factor divides 21 without leaving a remainder.

Steps to find Factors of 7 and 21

Step 1. Find all the numbers that would divide 7 and 21 without leaving any remainder. Starting with the number 1 upto 3 (half of 7) and 1 upto 10 (half of 21). The number 1 and the number itself are always factors of the given number.

7 ÷ 1 : Remainder = 0

21 ÷ 1 : Remainder = 0

7 ÷ 7 : Remainder = 0

21 ÷ 3 : Remainder = 0

21 ÷ 7 : Remainder = 0

21 ÷ 21 : Remainder = 0

Hence, Factors of 7 are 1 and 7

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

Examples of GCF

Sammy baked 7 chocolate cookies and 21 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 7 and 21.
GCF of 7 and 21 is 7.

A class has 7 boys and 21 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 7 and 21. Hence, GCF of 7 and 21 is 7.

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(7, 21) = ( 7 * 21 ) / LCM(7, 21) = 7.

What is the GCF of 7 and 21?

GCF of 7 and 21 is 7.

Ariel is making ready to eat meals to share with friends. She has 7 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 7 and 21. So the GCF of 7 and 21 is 7.

Mary has 7 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 7 and 21. Hence, the GCF of 7 and 21 or the greatest arrangement is 7.

Kamal is making identical balloon arrangements for a party. He has 7 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 7 and 21. So the GCF of 7 and 21 is 7.

Kunal is making baskets full of nuts and dried fruits. He has 7 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 7 and 21. So the GCF of 7 and 21 is 7.