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 (104, 120).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 104 and 120 is 8, where 8 is less than both 104 and 120.
- GCF of two consecutive numbers is always 1.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
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. 104 and 120 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 104 and also of 120.
- Every number is a factor of zero (0), since 104 x 0 = 0 and 120 x 0 = 0.
- 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, 4, 8, 13, 26, 52, 104 are exact divisors of 104 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 are exact divisors of 120.
- Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104. Each factor divides 104 without leaving a remainder.
Simlarly, factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Each factor divides 120 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 13, 26, 52, 104 are all less than or equal to 104 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 are all less than or equal to 120.
Steps to find Factors of 104 and 120
- Step 1. Find all the numbers that would divide 104 and 120 without leaving any remainder. Starting with the number 1 upto 52 (half of 104) and 1 upto 60 (half of 120). The number 1 and the number itself are always factors of the given number.
104 ÷ 1 : Remainder = 0
120 ÷ 1 : Remainder = 0
104 ÷ 2 : Remainder = 0
120 ÷ 2 : Remainder = 0
104 ÷ 4 : Remainder = 0
120 ÷ 3 : Remainder = 0
104 ÷ 8 : Remainder = 0
120 ÷ 4 : Remainder = 0
104 ÷ 13 : Remainder = 0
120 ÷ 5 : Remainder = 0
104 ÷ 26 : Remainder = 0
120 ÷ 6 : Remainder = 0
104 ÷ 52 : Remainder = 0
120 ÷ 8 : Remainder = 0
104 ÷ 104 : Remainder = 0
120 ÷ 10 : Remainder = 0
120 ÷ 120 : Remainder = 0
Hence, Factors of
104 are 1, 2, 4, 8, 13, 26, 52, and 104
And, Factors of
120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120
Examples of GCF
Sammy baked 104 chocolate cookies and 120 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 104 and 120.
GCF of 104 and 120 is 8.
A class has 104 boys and 120 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 104 and 120. Hence, GCF of 104 and 120 is 8.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(104, 120) = ( 104 * 120 ) / LCM(104, 120) = 8.
What is the GCF of 104 and 120?GCF of 104 and 120 is 8.
Ram has 104 cans of Pepsi and 120 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 104 and 120. Hence GCF of 104 and 120 is 8. So the number of tables that can be arranged is 8.
Rubel is creating individual servings of starters for her birthday party. He has 104 pizzas and 120 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 104 and 120. Thus GCF of 104 and 120 is 8.
Ariel is making ready to eat meals to share with friends. She has 104 bottles of water and 120 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 104 and 120. So the GCF of 104 and 120 is 8.
Kamal is making identical balloon arrangements for a party. He has 104 maroon balloons, and 120 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 104 and 120. So the GCF of 104 and 120 is 8.
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 104 bus tickets and 120 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 104 and 120. Hence, GCF of 104 and 120 is 8.