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 (100, 120).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 100 and 120 is 20, where 20 is less than both 100 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.
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. 100 and 120 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 100 and also of 120.
- Every number is a factor of zero (0), since 100 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, 5, 10, 20, 25, 50, 100 are exact divisors of 100 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 are exact divisors of 120.
- Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. Each factor divides 100 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, 5, 10, 20, 25, 50, 100 are all less than or equal to 100 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 100 and 120
- Step 1. Find all the numbers that would divide 100 and 120 without leaving any remainder. Starting with the number 1 upto 50 (half of 100) and 1 upto 60 (half of 120). The number 1 and the number itself are always factors of the given number.
100 ÷ 1 : Remainder = 0
120 ÷ 1 : Remainder = 0
100 ÷ 2 : Remainder = 0
120 ÷ 2 : Remainder = 0
100 ÷ 4 : Remainder = 0
120 ÷ 3 : Remainder = 0
100 ÷ 5 : Remainder = 0
120 ÷ 4 : Remainder = 0
100 ÷ 10 : Remainder = 0
120 ÷ 5 : Remainder = 0
100 ÷ 20 : Remainder = 0
120 ÷ 6 : Remainder = 0
100 ÷ 25 : Remainder = 0
120 ÷ 8 : Remainder = 0
100 ÷ 50 : Remainder = 0
120 ÷ 10 : Remainder = 0
100 ÷ 100 : Remainder = 0
120 ÷ 12 : Remainder = 0
120 ÷ 120 : Remainder = 0
Hence, Factors of
100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100
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 100 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 100 and 120.
GCF of 100 and 120 is 20.
A class has 100 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 100 and 120. Hence, GCF of 100 and 120 is 20.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(100, 120) = ( 100 * 120 ) / LCM(100, 120) = 20.
What is the GCF of 100 and 120?GCF of 100 and 120 is 20.
Ram has 100 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 100 and 120. Hence GCF of 100 and 120 is 20. So the number of tables that can be arranged is 20.
Mary has 100 blue buttons and 120 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 100 and 120. Hence, the GCF of 100 and 120 or the greatest arrangement is 20.
Kamal is making identical balloon arrangements for a party. He has 100 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 100 and 120. So the GCF of 100 and 120 is 20.
Kunal is making baskets full of nuts and dried fruits. He has 100 bags of nuts and 120 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 100 and 120. So the GCF of 100 and 120 is 20.
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 100 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 100 and 120. Hence, GCF of 100 and 120 is 20.