# What is GCF of 52 and 68?

GCF of 52 and 68 is 4

#### How to find GCF of two numbers

 1.   Steps to find GCF of 52 and 68 2.   What is GCF of two numbers? 3.   What are Factors? 4.   Examples of GCF

### Example: Find gcf of 52 and 68

• Factors for 52: 1, 2, 4, 13, 26, 52
• Factors for 68: 1, 2, 4, 17, 34, 68

Hence, GCf of 52 and 68 is 4

#### How do we define GCF?

In mathematics we use GCF or greatest common method to find out the greatest possible positive integer which can completely divide the given numbers. It is written as GCF (52, 68).

#### Properties of GCF

• The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 52 and 68 is 4, where 4 is less than both 52 and 68.
• 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 do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 52 and 68 are factors of themselves respectively.
• 1 is a factor of every number. Eg. 1 is a factor of 52 and also of 68.
• Every number is a factor of zero (0), since 52 x 0 = 0 and 68 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, 13, 26, 52 are exact divisors of 52 and 1, 2, 4, 17, 34, 68 are exact divisors of 68.
• Factors of 52 are 1, 2, 4, 13, 26, 52. Each factor divides 52 without leaving a remainder.
Simlarly, factors of 68 are 1, 2, 4, 17, 34, 68. Each factor divides 68 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 13, 26, 52 are all less than or equal to 52 and 1, 2, 4, 17, 34, 68 are all less than or equal to 68.

#### Steps to find Factors of 52 and 68

• Step 1. Find all the numbers that would divide 52 and 68 without leaving any remainder. Starting with the number 1 upto 26 (half of 52) and 1 upto 34 (half of 68). The number 1 and the number itself are always factors of the given number.
52 ÷ 1 : Remainder = 0
68 ÷ 1 : Remainder = 0
52 ÷ 2 : Remainder = 0
68 ÷ 2 : Remainder = 0
52 ÷ 4 : Remainder = 0
68 ÷ 4 : Remainder = 0
52 ÷ 13 : Remainder = 0
68 ÷ 17 : Remainder = 0
52 ÷ 26 : Remainder = 0
68 ÷ 34 : Remainder = 0
52 ÷ 52 : Remainder = 0
68 ÷ 68 : Remainder = 0

Hence, Factors of 52 are 1, 2, 4, 13, 26, and 52

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

#### Examples of GCF

Sammy baked 52 chocolate cookies and 68 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 52 and 68.
GCF of 52 and 68 is 4.

A class has 52 boys and 68 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 52 and 68. Hence, GCF of 52 and 68 is 4.

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(52, 68) = ( 52 * 68 ) / LCM(52, 68) = 4.

What is the GCF of 52 and 68?

GCF of 52 and 68 is 4.

Ariel is making ready to eat meals to share with friends. She has 52 bottles of water and 68 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 52 and 68. So the GCF of 52 and 68 is 4.

Mary has 52 blue buttons and 68 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 52 and 68. Hence, the GCF of 52 and 68 or the greatest arrangement is 4.

Kamal is making identical balloon arrangements for a party. He has 52 maroon balloons, and 68 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 52 and 68. So the GCF of 52 and 68 is 4.

Kunal is making baskets full of nuts and dried fruits. He has 52 bags of nuts and 68 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 52 and 68. So the GCF of 52 and 68 is 4.