What is GCF of 128 and 242?

Go back to 'All gcf of pages' >

GCF of 128 and 242 is 2

How to find GCF of two numbers

Steps to find GCF of 128 and 242

Find all the numbers that would divide 128 and 242 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 128 and 242, and read off the answer!

Example: Find gcf of 128 and 242

Factors for 128: 1, 2, 4, 8, 16, 32, 64, 128
Factors for 242: 1, 2, 11, 22, 121, 242

Hence, GCf of 128 and 242 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 (128, 242).

Properties of GCF

The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 128 and 242 is 2, where 2 is less than both 128 and 242.
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. 128 and 242 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 128 and also of 242.
Every number is a factor of zero (0), since 128 x 0 = 0 and 242 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, 16, 32, 64, 128 are exact divisors of 128 and 1, 2, 11, 22, 121, 242 are exact divisors of 242.
Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128. Each factor divides 128 without leaving a remainder.
Simlarly, factors of 242 are 1, 2, 11, 22, 121, 242. Each factor divides 242 without leaving a remainder.
Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32, 64, 128 are all less than or equal to 128 and 1, 2, 11, 22, 121, 242 are all less than or equal to 242.

Steps to find Factors of 128 and 242

Step 1. Find all the numbers that would divide 128 and 242 without leaving any remainder. Starting with the number 1 upto 64 (half of 128) and 1 upto 121 (half of 242). The number 1 and the number itself are always factors of the given number.

128 ÷ 1 : Remainder = 0

242 ÷ 1 : Remainder = 0

128 ÷ 2 : Remainder = 0

242 ÷ 2 : Remainder = 0

128 ÷ 4 : Remainder = 0

242 ÷ 11 : Remainder = 0

128 ÷ 8 : Remainder = 0

242 ÷ 22 : Remainder = 0

128 ÷ 16 : Remainder = 0

242 ÷ 121 : Remainder = 0

128 ÷ 32 : Remainder = 0

242 ÷ 242 : Remainder = 0

128 ÷ 64 : Remainder = 0

128 ÷ 128 : Remainder = 0

Hence, Factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128

And, Factors of 242 are 1, 2, 11, 22, 121, and 242

Examples of GCF

A class has 128 boys and 242 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 128 and 242. Hence, GCF of 128 and 242 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(128, 242) = ( 128 * 242 ) / LCM(128, 242) = 2.

What is the GCF of 128 and 242?

GCF of 128 and 242 is 2.

Ram has 128 cans of Pepsi and 242 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 128 and 242. Hence GCF of 128 and 242 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 128 pizzas and 242 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 128 and 242. Thus GCF of 128 and 242 is 2.

Ariel is making ready to eat meals to share with friends. She has 128 bottles of water and 242 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 128 and 242. So the GCF of 128 and 242 is 2.

Mary has 128 blue buttons and 242 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 128 and 242. Hence, the GCF of 128 and 242 or the greatest arrangement is 2.

Kunal is making baskets full of nuts and dried fruits. He has 128 bags of nuts and 242 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 128 and 242. So the GCF of 128 and 242 is 2.