What is GCF of 81 and 99?


Steps to find GCF of 81 and 99

Example: Find gcf of 81 and 99

  • Factors for 81: 1, 3, 9, 27, 81
  • Factors for 99: 1, 3, 9, 11, 33, 99

Hence, GCf of 81 and 99 is 9

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 (81, 99).

Properties of GCF

  • The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 81 and 99 is 9, where 9 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 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

  • Every factor of a number is an exact divisor of that number, example 1, 3, 9, 27, 81 are exact divisors of 81 and 1, 3, 9, 11, 33, 99 are exact divisors of 99.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 81 and 99 are factors of themselves respectively.
  • 1 is a factor of every number. Eg. 1 is a factor of 81 and also of 99.

Steps to find Factors of 81 and 99

  • Step 1. Find all the numbers that would divide 81 and 99 without leaving any remainder. Starting with the number 1 upto 40 (half of 81) and 1 upto 49 (half of 99). The number 1 and the number itself are always factors of the given number.
    81 ÷ 1 : Remainder = 0
    99 ÷ 1 : Remainder = 0
    81 ÷ 3 : Remainder = 0
    99 ÷ 3 : Remainder = 0
    81 ÷ 9 : Remainder = 0
    99 ÷ 9 : Remainder = 0
    81 ÷ 27 : Remainder = 0
    99 ÷ 11 : Remainder = 0
    81 ÷ 81 : Remainder = 0
    99 ÷ 33 : Remainder = 0
    99 ÷ 99 : Remainder = 0

Hence, Factors of 81 are 1, 3, 9, 27, and 81

And, Factors of 99 are 1, 3, 9, 11, 33, and 99

Examples of GCF

Sammy baked 81 chocolate cookies and 99 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 81 and 99.
GCF of 81 and 99 is 9.

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(81, 99) = ( 81 * 99 ) / LCM(81, 99) = 9.

What is the GCF of 81 and 99?

GCF of 81 and 99 is 9.

Ram has 81 cans of Pepsi and 99 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 81 and 99. Hence GCF of 81 and 99 is 9. So the number of tables that can be arranged is 9.

Rubel is creating individual servings of starters for her birthday party. He has 81 pizzas and 99 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 81 and 99. Thus GCF of 81 and 99 is 9.

Ariel is making ready to eat meals to share with friends. She has 81 bottles of water and 99 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 81 and 99. So the GCF of 81 and 99 is 9.

Mary has 81 blue buttons and 99 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 81 and 99. Hence, the GCF of 81 and 99 or the greatest arrangement is 9.

Kamal is making identical balloon arrangements for a party. He has 81 maroon balloons, and 99 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 81 and 99. So the GCF of 81 and 99 is 9.