What is GCF of 133 and 209?

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GCF of 133 and 209 is 19

How to find GCF of two numbers

Steps to find GCF of 133 and 209

Find all the numbers that would divide 133 and 209 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 133 and 209, and read off the answer!

Example: Find gcf of 133 and 209

Factors for 133: 1, 7, 19, 133
Factors for 209: 1, 11, 19, 209

Hence, GCf of 133 and 209 is 19

What does GCF mean in mathematics?

Greatest Common Fcator (GCF) or also sometimes written as greates common divisor is the largest number that can evenly divide the given two numbers. GCF is represented as GCF (133, 209).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 133 and 209 is 19, where 19 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 is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. 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, 7, 19, 133 are exact divisors of 133 and 1, 11, 19, 209 are exact divisors of 209.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 133 and 209 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 133 and also of 209.

Steps to find Factors of 133 and 209

Step 1. Find all the numbers that would divide 133 and 209 without leaving any remainder. Starting with the number 1 upto 66 (half of 133) and 1 upto 104 (half of 209). The number 1 and the number itself are always factors of the given number.

133 ÷ 1 : Remainder = 0

209 ÷ 1 : Remainder = 0

133 ÷ 7 : Remainder = 0

209 ÷ 11 : Remainder = 0

133 ÷ 19 : Remainder = 0

209 ÷ 19 : Remainder = 0

133 ÷ 133 : Remainder = 0

209 ÷ 209 : Remainder = 0

Hence, Factors of 133 are 1, 7, 19, and 133

And, Factors of 209 are 1, 11, 19, and 209

Examples of GCF

Sammy baked 133 chocolate cookies and 209 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 133 and 209.
GCF of 133 and 209 is 19.

A class has 133 boys and 209 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 133 and 209. Hence, GCF of 133 and 209 is 19.

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(133, 209) = ( 133 * 209 ) / LCM(133, 209) = 19.

What is the GCF of 133 and 209?

GCF of 133 and 209 is 19.

Ariel is making ready to eat meals to share with friends. She has 133 bottles of water and 209 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 133 and 209. So the GCF of 133 and 209 is 19.

Mary has 133 blue buttons and 209 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 133 and 209. Hence, the GCF of 133 and 209 or the greatest arrangement is 19.

Kamal is making identical balloon arrangements for a party. He has 133 maroon balloons, and 209 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 133 and 209. So the GCF of 133 and 209 is 19.

Kunal is making baskets full of nuts and dried fruits. He has 133 bags of nuts and 209 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 133 and 209. So the GCF of 133 and 209 is 19.