# What is GCF of 29 and 87?

GCF of 29 and 87 is 29

#### How to find GCF of two numbers

 1.   Steps to find GCF of 29 and 87 2.   What is GCF of two numbers? 3.   What are Factors? 4.   Examples of GCF

### Example: Find gcf of 29 and 87

• Factors for 29: 1, 29
• Factors for 87: 1, 3, 29, 87

Hence, GCf of 29 and 87 is 29

#### How do you explain GCF in mathematics?

GCF or greatest common factor of two or more numbers is defined as largest possible number or integer which is the factor of all given number or in other words we can say that largest possible common number which completely divides the given numbers. GCF of two numbers can be represented as GCF (29, 87).

#### Properties of GCF

• The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 29 and 87 is 29, where 29 is less than both the numbers.
• If the given numbers are consecutive than GCF is always 1.
• Product of two numbers is always equal to the product of their GCF and LCM.
• 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 number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of Factors

• Every factor of a number is an exact divisor of that number, example 1, 29 are exact divisors of 29 and 1, 3, 29, 87 are exact divisors of 87.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 29 and 87 are factors of themselves respectively.
• 1 is a factor of every number. Eg. 1 is a factor of 29 and also of 87.

#### Steps to find Factors of 29 and 87

• Step 1. Find all the numbers that would divide 29 and 87 without leaving any remainder. Starting with the number 1 upto 14 (half of 29) and 1 upto 43 (half of 87). The number 1 and the number itself are always factors of the given number.
29 ÷ 1 : Remainder = 0
87 ÷ 1 : Remainder = 0
29 ÷ 29 : Remainder = 0
87 ÷ 3 : Remainder = 0
87 ÷ 29 : Remainder = 0
87 ÷ 87 : Remainder = 0

Hence, Factors of 29 are 1 and 29

And, Factors of 87 are 1, 3, 29, and 87

#### Examples of GCF

A class has 29 boys and 87 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 29 and 87. Hence, GCF of 29 and 87 is 29.

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(29, 87) = ( 29 * 87 ) / LCM(29, 87) = 29.

What is the GCF of 29 and 87?

GCF of 29 and 87 is 29.

Ram has 29 cans of Pepsi and 87 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 29 and 87. Hence GCF of 29 and 87 is 29. So the number of tables that can be arranged is 29.

Rubel is creating individual servings of starters for her birthday party. He has 29 pizzas and 87 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 29 and 87. Thus GCF of 29 and 87 is 29.

Ariel is making ready to eat meals to share with friends. She has 29 bottles of water and 87 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 29 and 87. So the GCF of 29 and 87 is 29.

Mary has 29 blue buttons and 87 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 29 and 87. Hence, the GCF of 29 and 87 or the greatest arrangement is 29.

Kunal is making baskets full of nuts and dried fruits. He has 29 bags of nuts and 87 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 29 and 87. So the GCF of 29 and 87 is 29.