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 (75, 200).
Properties of GCF
- The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
- GCF of two consecutive numbers is always 1.
- Given two numbers 75 and 200, such that GCF is 25 where 25 will always be less than 75 and 200.
- Product of two numbers is always equal to the product of their GCF and LCM.
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
- Every number is a factor of zero (0), since 75 x 0 = 0 and 200 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, 3, 5, 15, 25, 75 are exact divisors of 75 and 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200 are exact divisors of 200.
- Factors of 75 are 1, 3, 5, 15, 25, 75. Each factor divides 75 without leaving a remainder.
Simlarly, factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. Each factor divides 200 without leaving a remainder.
Steps to find Factors of 75 and 200
- Step 1. Find all the numbers that would divide 75 and 200 without leaving any remainder. Starting with the number 1 upto 37 (half of 75) and 1 upto 100 (half of 200). The number 1 and the number itself are always factors of the given number.
75 ÷ 1 : Remainder = 0
200 ÷ 1 : Remainder = 0
75 ÷ 3 : Remainder = 0
200 ÷ 2 : Remainder = 0
75 ÷ 5 : Remainder = 0
200 ÷ 4 : Remainder = 0
75 ÷ 15 : Remainder = 0
200 ÷ 5 : Remainder = 0
75 ÷ 25 : Remainder = 0
200 ÷ 8 : Remainder = 0
75 ÷ 75 : Remainder = 0
200 ÷ 10 : Remainder = 0
200 ÷ 100 : Remainder = 0
200 ÷ 200 : Remainder = 0
Hence, Factors of
75 are 1, 3, 5, 15, 25, and 75
And, Factors of
200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200
Examples of GCF
Sammy baked 75 chocolate cookies and 200 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 75 and 200.
GCF of 75 and 200 is 25.
A class has 75 boys and 200 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 75 and 200. Hence, GCF of 75 and 200 is 25.
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.
Ram has 75 cans of Pepsi and 200 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 75 and 200. Hence GCF of 75 and 200 is 25. So the number of tables that can be arranged is 25.
Ariel is making ready to eat meals to share with friends. She has 75 bottles of water and 200 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 75 and 200. So the GCF of 75 and 200 is 25.
Mary has 75 blue buttons and 200 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 75 and 200. Hence, the GCF of 75 and 200 or the greatest arrangement is 25.
Kamal is making identical balloon arrangements for a party. He has 75 maroon balloons, and 200 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 75 and 200. So the GCF of 75 and 200 is 25.
Kunal is making baskets full of nuts and dried fruits. He has 75 bags of nuts and 200 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 75 and 200. So the GCF of 75 and 200 is 25.
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 75 bus tickets and 200 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 75 and 200. Hence, GCF of 75 and 200 is 25.