What is GCF of 76 and 114?

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GCF of 76 and 114 is 38

How to find GCF of two numbers

Steps to find GCF of 76 and 114

Find all the numbers that would divide 76 and 114 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 76 and 114, and read off the answer!

Example: Find gcf of 76 and 114

Factors for 76: 1, 2, 4, 19, 38, 76
Factors for 114: 1, 2, 3, 6, 19, 38, 57, 114

Hence, GCf of 76 and 114 is 38

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 (76, 114).

Properties of GCF

The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 76 and 114 is 38, where 38 is less than both 76 and 114.
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.

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

Each number is a factor of itself. Eg. 76 and 114 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 76 and also of 114.
Every number is a factor of zero (0), since 76 x 0 = 0 and 114 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, 19, 38, 76 are exact divisors of 76 and 1, 2, 3, 6, 19, 38, 57, 114 are exact divisors of 114.
Factors of 76 are 1, 2, 4, 19, 38, 76. Each factor divides 76 without leaving a remainder.
Simlarly, factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. Each factor divides 114 without leaving a remainder.
Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 19, 38, 76 are all less than or equal to 76 and 1, 2, 3, 6, 19, 38, 57, 114 are all less than or equal to 114.

Steps to find Factors of 76 and 114

Step 1. Find all the numbers that would divide 76 and 114 without leaving any remainder. Starting with the number 1 upto 38 (half of 76) and 1 upto 57 (half of 114). The number 1 and the number itself are always factors of the given number.

76 ÷ 1 : Remainder = 0

114 ÷ 1 : Remainder = 0

76 ÷ 2 : Remainder = 0

114 ÷ 2 : Remainder = 0

76 ÷ 4 : Remainder = 0

114 ÷ 3 : Remainder = 0

76 ÷ 19 : Remainder = 0

114 ÷ 6 : Remainder = 0

76 ÷ 38 : Remainder = 0

114 ÷ 19 : Remainder = 0

76 ÷ 76 : Remainder = 0

114 ÷ 38 : Remainder = 0

114 ÷ 57 : Remainder = 0

114 ÷ 114 : Remainder = 0

Hence, Factors of 76 are 1, 2, 4, 19, 38, and 76

And, Factors of 114 are 1, 2, 3, 6, 19, 38, 57, and 114

Examples of GCF

Sammy baked 76 chocolate cookies and 114 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 76 and 114.
GCF of 76 and 114 is 38.

A class has 76 boys and 114 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 76 and 114. Hence, GCF of 76 and 114 is 38.

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(76, 114) = ( 76 * 114 ) / LCM(76, 114) = 38.

What is the GCF of 76 and 114?

GCF of 76 and 114 is 38.

Mary has 76 blue buttons and 114 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 76 and 114. Hence, the GCF of 76 and 114 or the greatest arrangement is 38.

Kamal is making identical balloon arrangements for a party. He has 76 maroon balloons, and 114 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 76 and 114. So the GCF of 76 and 114 is 38.

Kunal is making baskets full of nuts and dried fruits. He has 76 bags of nuts and 114 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 76 and 114. So the GCF of 76 and 114 is 38.

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 76 bus tickets and 114 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 76 and 114. Hence, GCF of 76 and 114 is 38.