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 (110, 306).
Properties of GCF
- Given two numbers 110 and 306, such that GCF is 2 where 2 will always be less than 110 and 306.
- GCF of two numbers is always equal to 1 in case given numbers are consecutive.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- The GCF of two given numbers is either 1 or the number itself if one of them is a prime number.
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
- Each number is a factor of itself. Eg. 110 and 306 are factors of themselves respectively.
- 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, 2, 5, 10, 11, 22, 55, 110 are exact divisors of 110 and 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306 are exact divisors of 306.
- 1 is a factor of every number. Eg. 1 is a factor of 110 and also of 306.
- Every number is a factor of zero (0), since 110 x 0 = 0 and 306 x 0 = 0.
Steps to find Factors of 110 and 306
- Step 1. Find all the numbers that would divide 110 and 306 without leaving any remainder. Starting with the number 1 upto 55 (half of 110) and 1 upto 153 (half of 306). The number 1 and the number itself are always factors of the given number.
110 ÷ 1 : Remainder = 0
306 ÷ 1 : Remainder = 0
110 ÷ 2 : Remainder = 0
306 ÷ 2 : Remainder = 0
110 ÷ 5 : Remainder = 0
306 ÷ 3 : Remainder = 0
110 ÷ 10 : Remainder = 0
306 ÷ 6 : Remainder = 0
110 ÷ 11 : Remainder = 0
306 ÷ 9 : Remainder = 0
110 ÷ 22 : Remainder = 0
306 ÷ 17 : Remainder = 0
110 ÷ 55 : Remainder = 0
306 ÷ 18 : Remainder = 0
110 ÷ 110 : Remainder = 0
306 ÷ 34 : Remainder = 0
306 ÷ 102 : Remainder = 0
306 ÷ 153 : Remainder = 0
306 ÷ 306 : Remainder = 0
Hence, Factors of
110 are 1, 2, 5, 10, 11, 22, 55, and 110
And, Factors of
306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306
Examples of GCF
A class has 110 boys and 306 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 110 and 306. Hence, GCF of 110 and 306 is 2.
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(110, 306) = ( 110 * 306 ) / LCM(110, 306) = 2.
What is the GCF of 110 and 306?GCF of 110 and 306 is 2.
Ram has 110 cans of Pepsi and 306 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 110 and 306. Hence GCF of 110 and 306 is 2. So the number of tables that can be arranged is 2.
Rubel is creating individual servings of starters for her birthday party. He has 110 pizzas and 306 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 110 and 306. Thus GCF of 110 and 306 is 2.
Ariel is making ready to eat meals to share with friends. She has 110 bottles of water and 306 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 110 and 306. So the GCF of 110 and 306 is 2.
Mary has 110 blue buttons and 306 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 110 and 306. Hence, the GCF of 110 and 306 or the greatest arrangement is 2.
Kunal is making baskets full of nuts and dried fruits. He has 110 bags of nuts and 306 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 110 and 306. So the GCF of 110 and 306 is 2.