What is GCF of 189 and 351?

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GCF of 189 and 351 is 27

How to find GCF of two numbers

Steps to find GCF of 189 and 351

Find all the numbers that would divide 189 and 351 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 189 and 351, and read off the answer!

Example: Find gcf of 189 and 351

Factors for 189: 1, 3, 7, 9, 21, 27, 63, 189
Factors for 351: 1, 3, 9, 13, 27, 39, 117, 351

Hence, GCf of 189 and 351 is 27

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 (189, 351).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 189 and 351 is 27, where 27 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, 3, 7, 9, 21, 27, 63, 189 are exact divisors of 189 and 1, 3, 9, 13, 27, 39, 117, 351 are exact divisors of 351.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 189 and 351 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 189 and also of 351.

Steps to find Factors of 189 and 351

Step 1. Find all the numbers that would divide 189 and 351 without leaving any remainder. Starting with the number 1 upto 94 (half of 189) and 1 upto 175 (half of 351). The number 1 and the number itself are always factors of the given number.

189 ÷ 1 : Remainder = 0

351 ÷ 1 : Remainder = 0

189 ÷ 3 : Remainder = 0

351 ÷ 3 : Remainder = 0

189 ÷ 7 : Remainder = 0

351 ÷ 9 : Remainder = 0

189 ÷ 9 : Remainder = 0

351 ÷ 13 : Remainder = 0

189 ÷ 21 : Remainder = 0

351 ÷ 27 : Remainder = 0

189 ÷ 27 : Remainder = 0

351 ÷ 39 : Remainder = 0

189 ÷ 63 : Remainder = 0

351 ÷ 117 : Remainder = 0

189 ÷ 189 : Remainder = 0

351 ÷ 351 : Remainder = 0

Hence, Factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189

And, Factors of 351 are 1, 3, 9, 13, 27, 39, 117, and 351

Examples of GCF

Sammy baked 189 chocolate cookies and 351 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 189 and 351.
GCF of 189 and 351 is 27.

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(189, 351) = ( 189 * 351 ) / LCM(189, 351) = 27.

What is the GCF of 189 and 351?

GCF of 189 and 351 is 27.

Ram has 189 cans of Pepsi and 351 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 189 and 351. Hence GCF of 189 and 351 is 27. So the number of tables that can be arranged is 27.

Rubel is creating individual servings of starters for her birthday party. He has 189 pizzas and 351 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 189 and 351. Thus GCF of 189 and 351 is 27.

Ariel is making ready to eat meals to share with friends. She has 189 bottles of water and 351 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 189 and 351. So the GCF of 189 and 351 is 27.

Mary has 189 blue buttons and 351 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 189 and 351. Hence, the GCF of 189 and 351 or the greatest arrangement is 27.

Kamal is making identical balloon arrangements for a party. He has 189 maroon balloons, and 351 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 189 and 351. So the GCF of 189 and 351 is 27.