What is GCF of 98 and 112?

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GCF of 98 and 112 is 14

How to find GCF of two numbers

Steps to find GCF of 98 and 112

Find all the numbers that would divide 98 and 112 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 98 and 112, and read off the answer!

Example: Find gcf of 98 and 112

Factors for 98: 1, 2, 7, 14, 49, 98
Factors for 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

Hence, GCf of 98 and 112 is 14

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 (98, 112).

Properties of GCF

Given two numbers 98 and 112, such that GCF is 14 where 14 will always be less than 98 and 112.
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.

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. 98 and 112 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, 7, 14, 49, 98 are exact divisors of 98 and 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 are exact divisors of 112.
1 is a factor of every number. Eg. 1 is a factor of 98 and also of 112.
Every number is a factor of zero (0), since 98 x 0 = 0 and 112 x 0 = 0.

Steps to find Factors of 98 and 112

Step 1. Find all the numbers that would divide 98 and 112 without leaving any remainder. Starting with the number 1 upto 49 (half of 98) and 1 upto 56 (half of 112). The number 1 and the number itself are always factors of the given number.

98 ÷ 1 : Remainder = 0

112 ÷ 1 : Remainder = 0

98 ÷ 2 : Remainder = 0

112 ÷ 2 : Remainder = 0

98 ÷ 7 : Remainder = 0

112 ÷ 4 : Remainder = 0

98 ÷ 14 : Remainder = 0

112 ÷ 7 : Remainder = 0

98 ÷ 49 : Remainder = 0

112 ÷ 8 : Remainder = 0

98 ÷ 98 : Remainder = 0

112 ÷ 14 : Remainder = 0

112 ÷ 16 : Remainder = 0

112 ÷ 28 : Remainder = 0

112 ÷ 56 : Remainder = 0

112 ÷ 112 : Remainder = 0

Hence, Factors of 98 are 1, 2, 7, 14, 49, and 98

And, Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112

Examples of GCF

Sammy baked 98 chocolate cookies and 112 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 98 and 112.
GCF of 98 and 112 is 14.

A class has 98 boys and 112 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 98 and 112. Hence, GCF of 98 and 112 is 14.

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(98, 112) = ( 98 * 112 ) / LCM(98, 112) = 14.

What is the GCF of 98 and 112?

GCF of 98 and 112 is 14.

Ariel is making ready to eat meals to share with friends. She has 98 bottles of water and 112 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 98 and 112. So the GCF of 98 and 112 is 14.

Mary has 98 blue buttons and 112 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 98 and 112. Hence, the GCF of 98 and 112 or the greatest arrangement is 14.

Kamal is making identical balloon arrangements for a party. He has 98 maroon balloons, and 112 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 98 and 112. So the GCF of 98 and 112 is 14.

Kunal is making baskets full of nuts and dried fruits. He has 98 bags of nuts and 112 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 98 and 112. So the GCF of 98 and 112 is 14.