What is GCF of 27 and 51?

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GCF of 27 and 51 is 3

How to find GCF of two numbers

Steps to find GCF of 27 and 51

Find all the numbers that would divide 27 and 51 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 27 and 51, and read off the answer!

Example: Find gcf of 27 and 51

Factors for 27: 1, 3, 9, 27
Factors for 51: 1, 3, 17, 51

Hence, GCf of 27 and 51 is 3

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 (27, 51).

Properties of GCF

The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
GCF of two consecutive numbers is always 1.
Given two numbers 27 and 51, such that GCF is 3 where 3 will always be less than 27 and 51.
Product of two numbers is always equal to the product of their GCF and LCM.

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

Every number is a factor of zero (0), since 27 x 0 = 0 and 51 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, 3, 9, 27 are exact divisors of 27 and 1, 3, 17, 51 are exact divisors of 51.
Factors of 27 are 1, 3, 9, 27. Each factor divides 27 without leaving a remainder.
Simlarly, factors of 51 are 1, 3, 17, 51. Each factor divides 51 without leaving a remainder.

Steps to find Factors of 27 and 51

Step 1. Find all the numbers that would divide 27 and 51 without leaving any remainder. Starting with the number 1 upto 13 (half of 27) and 1 upto 25 (half of 51). The number 1 and the number itself are always factors of the given number.

27 ÷ 1 : Remainder = 0

51 ÷ 1 : Remainder = 0

27 ÷ 3 : Remainder = 0

51 ÷ 3 : Remainder = 0

27 ÷ 9 : Remainder = 0

51 ÷ 17 : Remainder = 0

27 ÷ 27 : Remainder = 0

51 ÷ 51 : Remainder = 0

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

And, Factors of 51 are 1, 3, 17, and 51

Examples of GCF

Sammy baked 27 chocolate cookies and 51 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 27 and 51.
GCF of 27 and 51 is 3.

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(27, 51) = ( 27 * 51 ) / LCM(27, 51) = 3.

What is the GCF of 27 and 51?

GCF of 27 and 51 is 3.

Ram has 27 cans of Pepsi and 51 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 27 and 51. Hence GCF of 27 and 51 is 3. So the number of tables that can be arranged is 3.

Rubel is creating individual servings of starters for her birthday party. He has 27 pizzas and 51 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 27 and 51. Thus GCF of 27 and 51 is 3.

Ariel is making ready to eat meals to share with friends. She has 27 bottles of water and 51 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 27 and 51. So the GCF of 27 and 51 is 3.

Mary has 27 blue buttons and 51 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 27 and 51. Hence, the GCF of 27 and 51 or the greatest arrangement is 3.

Kamal is making identical balloon arrangements for a party. He has 27 maroon balloons, and 51 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 27 and 51. So the GCF of 27 and 51 is 3.