What is GCF of 165 and 231?

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GCF of 165 and 231 is 33

How to find GCF of two numbers

Steps to find GCF of 165 and 231

Find all the numbers that would divide 165 and 231 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 165 and 231, and read off the answer!

Example: Find gcf of 165 and 231

Factors for 165: 1, 3, 5, 11, 15, 33, 55, 165
Factors for 231: 1, 3, 7, 11, 21, 33, 77, 231

Hence, GCf of 165 and 231 is 33

Definition of GCF

Greatest common factor commonly known as GCF of the two numbers is the highest possible number which completely divides given numbers, i.e. without leaving any remainder. It is represented as GCF (165, 231).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 165 and 231 is 33, where 33 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.

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of Factors

Every factor of a number is an exact divisor of that number, example 1, 3, 5, 11, 15, 33, 55, 165 are exact divisors of 165 and 1, 3, 7, 11, 21, 33, 77, 231 are exact divisors of 231.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 165 and 231 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 165 and also of 231.

Steps to find Factors of 165 and 231

Step 1. Find all the numbers that would divide 165 and 231 without leaving any remainder. Starting with the number 1 upto 82 (half of 165) and 1 upto 115 (half of 231). The number 1 and the number itself are always factors of the given number.

165 ÷ 1 : Remainder = 0

231 ÷ 1 : Remainder = 0

165 ÷ 3 : Remainder = 0

231 ÷ 3 : Remainder = 0

165 ÷ 5 : Remainder = 0

231 ÷ 7 : Remainder = 0

165 ÷ 11 : Remainder = 0

231 ÷ 11 : Remainder = 0

165 ÷ 15 : Remainder = 0

231 ÷ 21 : Remainder = 0

165 ÷ 33 : Remainder = 0

231 ÷ 33 : Remainder = 0

165 ÷ 55 : Remainder = 0

231 ÷ 77 : Remainder = 0

165 ÷ 165 : Remainder = 0

231 ÷ 231 : Remainder = 0

Hence, Factors of 165 are 1, 3, 5, 11, 15, 33, 55, and 165

And, Factors of 231 are 1, 3, 7, 11, 21, 33, 77, and 231

Examples of GCF

Sammy baked 165 chocolate cookies and 231 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 165 and 231.
GCF of 165 and 231 is 33.

A class has 165 boys and 231 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 165 and 231. Hence, GCF of 165 and 231 is 33.

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.

Ram has 165 cans of Pepsi and 231 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 165 and 231. Hence GCF of 165 and 231 is 33. So the number of tables that can be arranged is 33.

Ariel is making ready to eat meals to share with friends. She has 165 bottles of water and 231 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 165 and 231. So the GCF of 165 and 231 is 33.

Mary has 165 blue buttons and 231 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 165 and 231. Hence, the GCF of 165 and 231 or the greatest arrangement is 33.

Kamal is making identical balloon arrangements for a party. He has 165 maroon balloons, and 231 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 165 and 231. So the GCF of 165 and 231 is 33.

Kunal is making baskets full of nuts and dried fruits. He has 165 bags of nuts and 231 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 165 and 231. So the GCF of 165 and 231 is 33.

To energize public transportation, Abir needs to give a few companions envelopes with transport tickets, and metro tickets in them. On the off chance that he has 165 bus tickets and 231 metro tickets to be parted similarly among the envelopes, and he need no tickets left. What is the greatest number of envelopes Abir can make?

To make the greatest number of envelopes Abir needs to find out the GCF of 165 and 231. Hence, GCF of 165 and 231 is 33.