What is GCF of 68 and 102?

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GCF of 68 and 102 is 34

How to find GCF of two numbers

Steps to find GCF of 68 and 102

Find all the numbers that would divide 68 and 102 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 68 and 102, and read off the answer!

Example: Find gcf of 68 and 102

Factors for 68: 1, 2, 4, 17, 34, 68
Factors for 102: 1, 2, 3, 6, 17, 34, 51, 102

Hence, GCf of 68 and 102 is 34

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 (68, 102).

Properties of GCF

The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 68 and 102 is 34, where 34 is less than both 68 and 102.
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. 68 and 102 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 68 and also of 102.
Every number is a factor of zero (0), since 68 x 0 = 0 and 102 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, 17, 34, 68 are exact divisors of 68 and 1, 2, 3, 6, 17, 34, 51, 102 are exact divisors of 102.
Factors of 68 are 1, 2, 4, 17, 34, 68. Each factor divides 68 without leaving a remainder.
Simlarly, factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. Each factor divides 102 without leaving a remainder.
Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 17, 34, 68 are all less than or equal to 68 and 1, 2, 3, 6, 17, 34, 51, 102 are all less than or equal to 102.

Steps to find Factors of 68 and 102

Step 1. Find all the numbers that would divide 68 and 102 without leaving any remainder. Starting with the number 1 upto 34 (half of 68) and 1 upto 51 (half of 102). The number 1 and the number itself are always factors of the given number.

68 ÷ 1 : Remainder = 0

102 ÷ 1 : Remainder = 0

68 ÷ 2 : Remainder = 0

102 ÷ 2 : Remainder = 0

68 ÷ 4 : Remainder = 0

102 ÷ 3 : Remainder = 0

68 ÷ 17 : Remainder = 0

102 ÷ 6 : Remainder = 0

68 ÷ 34 : Remainder = 0

102 ÷ 17 : Remainder = 0

68 ÷ 68 : Remainder = 0

102 ÷ 34 : Remainder = 0

102 ÷ 51 : Remainder = 0

102 ÷ 102 : Remainder = 0

Hence, Factors of 68 are 1, 2, 4, 17, 34, and 68

And, Factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102

Examples of GCF

Sammy baked 68 chocolate cookies and 102 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 68 and 102.
GCF of 68 and 102 is 34.

A class has 68 boys and 102 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 68 and 102. Hence, GCF of 68 and 102 is 34.

What is the relation between LCM and GCF (Greatest Common Factor)?

GCF and LCM of two numbers can be related as GCF(68, 102) = ( 68 * 102 ) / LCM(68, 102) = 34.

What is the GCF of 68 and 102?

GCF of 68 and 102 is 34.

Ram has 68 cans of Pepsi and 102 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 68 and 102. Hence GCF of 68 and 102 is 34. So the number of tables that can be arranged is 34.

Rubel is creating individual servings of starters for her birthday party. He has 68 pizzas and 102 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 68 and 102. Thus GCF of 68 and 102 is 34.

Ariel is making ready to eat meals to share with friends. She has 68 bottles of water and 102 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 68 and 102. So the GCF of 68 and 102 is 34.

Kamal is making identical balloon arrangements for a party. He has 68 maroon balloons, and 102 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 68 and 102. So the GCF of 68 and 102 is 34.

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 68 bus tickets and 102 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 68 and 102. Hence, GCF of 68 and 102 is 34.