What is GCF of 21 and 35?

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GCF of 21 and 35 is 7

How to find GCF of two numbers

Steps to find GCF of 21 and 35

Find all the numbers that would divide 21 and 35 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 21 and 35, and read off the answer!

Example: Find gcf of 21 and 35

Factors for 21: 1, 3, 7, 21
Factors for 35: 1, 5, 7, 35

Hence, GCf of 21 and 35 is 7

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 (21, 35).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 21 and 35 is 7, where 7 is less than both the numbers.
If the given numbers are consecutive than GCF is always 1.
Product of two numbers is always equal to the product of their GCF and LCM.
The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.

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

Every factor of a number is an exact divisor of that number, example 1, 3, 7, 21 are exact divisors of 21 and 1, 5, 7, 35 are exact divisors of 35.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 21 and 35 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 21 and also of 35.

Steps to find Factors of 21 and 35

Step 1. Find all the numbers that would divide 21 and 35 without leaving any remainder. Starting with the number 1 upto 10 (half of 21) and 1 upto 17 (half of 35). The number 1 and the number itself are always factors of the given number.

21 ÷ 1 : Remainder = 0

35 ÷ 1 : Remainder = 0

21 ÷ 3 : Remainder = 0

35 ÷ 5 : Remainder = 0

21 ÷ 7 : Remainder = 0

35 ÷ 7 : Remainder = 0

21 ÷ 21 : Remainder = 0

35 ÷ 35 : Remainder = 0

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

And, Factors of 35 are 1, 5, 7, and 35

Examples of GCF

Sammy baked 21 chocolate cookies and 35 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 21 and 35.
GCF of 21 and 35 is 7.

A class has 21 boys and 35 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 21 and 35. Hence, GCF of 21 and 35 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.

Ram has 21 cans of Pepsi and 35 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 21 and 35. Hence GCF of 21 and 35 is 7. So the number of tables that can be arranged is 7.

Ariel is making ready to eat meals to share with friends. She has 21 bottles of water and 35 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 21 and 35. So the GCF of 21 and 35 is 7.

Mary has 21 blue buttons and 35 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 21 and 35. Hence, the GCF of 21 and 35 or the greatest arrangement is 7.

Kamal is making identical balloon arrangements for a party. He has 21 maroon balloons, and 35 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 21 and 35. So the GCF of 21 and 35 is 7.

Kunal is making baskets full of nuts and dried fruits. He has 21 bags of nuts and 35 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 21 and 35. So the GCF of 21 and 35 is 7.

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 21 bus tickets and 35 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 21 and 35. Hence, GCF of 21 and 35 is 7.