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 (14, 84).
Properties of GCF
- Given two numbers 14 and 84, such that GCF is 14 where 14 will always be less than 14 and 84.
- 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. 14 and 84 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, 7, 14 are exact divisors of 14 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 are exact divisors of 84.
- 1 is a factor of every number. Eg. 1 is a factor of 14 and also of 84.
- Every number is a factor of zero (0), since 14 x 0 = 0 and 84 x 0 = 0.
Steps to find Factors of 14 and 84
- Step 1. Find all the numbers that would divide 14 and 84 without leaving any remainder. Starting with the number 1 upto 7 (half of 14) and 1 upto 42 (half of 84). The number 1 and the number itself are always factors of the given number.
14 ÷ 1 : Remainder = 0
84 ÷ 1 : Remainder = 0
14 ÷ 2 : Remainder = 0
84 ÷ 2 : Remainder = 0
14 ÷ 7 : Remainder = 0
84 ÷ 3 : Remainder = 0
14 ÷ 14 : Remainder = 0
84 ÷ 4 : Remainder = 0
Hence, Factors of
14 are 1, 2, 7, and 14
And, Factors of
84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84
Examples of GCF
Sammy baked 14 chocolate cookies and 84 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 14 and 84.
GCF of 14 and 84 is 14.
A class has 14 boys and 84 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 14 and 84. Hence, GCF of 14 and 84 is 14.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(14, 84) = ( 14 * 84 ) / LCM(14, 84) = 14.
What is the GCF of 14 and 84?GCF of 14 and 84 is 14.
Ram has 14 cans of Pepsi and 84 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 14 and 84. Hence GCF of 14 and 84 is 14. So the number of tables that can be arranged is 14.
Rubel is creating individual servings of starters for her birthday party. He has 14 pizzas and 84 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 14 and 84. Thus GCF of 14 and 84 is 14.
Ariel is making ready to eat meals to share with friends. She has 14 bottles of water and 84 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 14 and 84. So the GCF of 14 and 84 is 14.
Kamal is making identical balloon arrangements for a party. He has 14 maroon balloons, and 84 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 14 and 84. So the GCF of 14 and 84 is 14.
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 14 bus tickets and 84 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 14 and 84. Hence, GCF of 14 and 84 is 14.