What is GCF of 20 and 74?

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GCF of 20 and 74 is 2

How to find GCF of two numbers

Steps to find GCF of 20 and 74

Find all the numbers that would divide 20 and 74 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 20 and 74, and read off the answer!

Example: Find gcf of 20 and 74

Factors for 20: 1, 2, 4, 5, 10, 20
Factors for 74: 1, 2, 37, 74

Hence, GCf of 20 and 74 is 2

Definition of GCF

Greatest common factor commonly known as GCF of the two numbers is the highest possible number which completely divides given numbers, i.e. without leaving any remainder. It is represented as GCF (20, 74).

Properties of GCF

The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 20 and 74 is 2, where 2 is less than both 20 and 74.
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 are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of Factors

Each number is a factor of itself. Eg. 20 and 74 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 20 and also of 74.
Every number is a factor of zero (0), since 20 x 0 = 0 and 74 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, 5, 10, 20 are exact divisors of 20 and 1, 2, 37, 74 are exact divisors of 74.
Factors of 20 are 1, 2, 4, 5, 10, 20. Each factor divides 20 without leaving a remainder.
Simlarly, factors of 74 are 1, 2, 37, 74. Each factor divides 74 without leaving a remainder.
Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 10, 20 are all less than or equal to 20 and 1, 2, 37, 74 are all less than or equal to 74.

Steps to find Factors of 20 and 74

Step 1. Find all the numbers that would divide 20 and 74 without leaving any remainder. Starting with the number 1 upto 10 (half of 20) and 1 upto 37 (half of 74). The number 1 and the number itself are always factors of the given number.

20 ÷ 1 : Remainder = 0

74 ÷ 1 : Remainder = 0

20 ÷ 2 : Remainder = 0

74 ÷ 2 : Remainder = 0

20 ÷ 4 : Remainder = 0

74 ÷ 37 : Remainder = 0

20 ÷ 5 : Remainder = 0

74 ÷ 74 : Remainder = 0

20 ÷ 10 : Remainder = 0

20 ÷ 20 : Remainder = 0

Hence, Factors of 20 are 1, 2, 4, 5, 10, and 20

And, Factors of 74 are 1, 2, 37, and 74

Examples of GCF

A class has 20 boys and 74 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 20 and 74. Hence, GCF of 20 and 74 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(20, 74) = ( 20 * 74 ) / LCM(20, 74) = 2.

What is the GCF of 20 and 74?

GCF of 20 and 74 is 2.

Ram has 20 cans of Pepsi and 74 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 20 and 74. Hence GCF of 20 and 74 is 2. So the number of tables that can be arranged is 2.

Rubel is creating individual servings of starters for her birthday party. He has 20 pizzas and 74 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 20 and 74. Thus GCF of 20 and 74 is 2.

Ariel is making ready to eat meals to share with friends. She has 20 bottles of water and 74 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 20 and 74. So the GCF of 20 and 74 is 2.

Mary has 20 blue buttons and 74 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 20 and 74. Hence, the GCF of 20 and 74 or the greatest arrangement is 2.

Kunal is making baskets full of nuts and dried fruits. He has 20 bags of nuts and 74 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 20 and 74. So the GCF of 20 and 74 is 2.