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 (374, 918).
Properties of GCF
- Given two numbers 374 and 918, such that GCF is 34 where 34 will always be less than 374 and 918.
- 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.
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
- Each number is a factor of itself. Eg. 374 and 918 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, 11, 17, 22, 34, 187, 374 are exact divisors of 374 and 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, 918 are exact divisors of 918.
- 1 is a factor of every number. Eg. 1 is a factor of 374 and also of 918.
- Every number is a factor of zero (0), since 374 x 0 = 0 and 918 x 0 = 0.
Steps to find Factors of 374 and 918
- Step 1. Find all the numbers that would divide 374 and 918 without leaving any remainder. Starting with the number 1 upto 187 (half of 374) and 1 upto 459 (half of 918). The number 1 and the number itself are always factors of the given number.
374 ÷ 1 : Remainder = 0
918 ÷ 1 : Remainder = 0
374 ÷ 2 : Remainder = 0
918 ÷ 2 : Remainder = 0
374 ÷ 11 : Remainder = 0
918 ÷ 3 : Remainder = 0
374 ÷ 17 : Remainder = 0
918 ÷ 6 : Remainder = 0
374 ÷ 22 : Remainder = 0
918 ÷ 9 : Remainder = 0
374 ÷ 34 : Remainder = 0
918 ÷ 17 : Remainder = 0
374 ÷ 187 : Remainder = 0
918 ÷ 18 : Remainder = 0
374 ÷ 374 : Remainder = 0
918 ÷ 27 : Remainder = 0
918 ÷ 102 : Remainder = 0
918 ÷ 153 : Remainder = 0
918 ÷ 306 : Remainder = 0
918 ÷ 459 : Remainder = 0
918 ÷ 918 : Remainder = 0
Hence, Factors of
374 are 1, 2, 11, 17, 22, 34, 187, and 374
And, Factors of
918 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, and 918
Examples of GCF
Sammy baked 374 chocolate cookies and 918 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 374 and 918.
GCF of 374 and 918 is 34.
A class has 374 boys and 918 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 374 and 918. Hence, GCF of 374 and 918 is 34.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(374, 918) = ( 374 * 918 ) / LCM(374, 918) = 34.
What is the GCF of 374 and 918?GCF of 374 and 918 is 34.
Ram has 374 cans of Pepsi and 918 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 374 and 918. Hence GCF of 374 and 918 is 34. So the number of tables that can be arranged is 34.
Rubel is creating individual servings of starters for her birthday party. He has 374 pizzas and 918 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 374 and 918. Thus GCF of 374 and 918 is 34.
Ariel is making ready to eat meals to share with friends. She has 374 bottles of water and 918 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 374 and 918. So the GCF of 374 and 918 is 34.
Kamal is making identical balloon arrangements for a party. He has 374 maroon balloons, and 918 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 374 and 918. So the GCF of 374 and 918 is 34.
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 374 bus tickets and 918 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 374 and 918. Hence, GCF of 374 and 918 is 34.