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 (12500, 800).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 12500 and 800 is 100, where 100 is less than both 12500 and 800.
- 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. 12500 and 800 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 12500 and also of 800.
- Every number is a factor of zero (0), since 12500 x 0 = 0 and 800 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, 125, 250, 500, 625, 1250, 2500, 3125, 6250, 12500 are exact divisors of 12500 and 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800 are exact divisors of 800.
- Factors of 12500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500, 3125, 6250, 12500. Each factor divides 12500 without leaving a remainder.
Simlarly, factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800. Each factor divides 800 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, 125, 250, 500, 625, 1250, 2500, 3125, 6250, 12500 are all less than or equal to 12500 and 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800 are all less than or equal to 800.
Steps to find Factors of 12500 and 800
- Step 1. Find all the numbers that would divide 12500 and 800 without leaving any remainder. Starting with the number 1 upto 6250 (half of 12500) and 1 upto 400 (half of 800). The number 1 and the number itself are always factors of the given number.
12500 ÷ 1 : Remainder = 0
800 ÷ 1 : Remainder = 0
12500 ÷ 2 : Remainder = 0
800 ÷ 2 : Remainder = 0
12500 ÷ 4 : Remainder = 0
800 ÷ 4 : Remainder = 0
12500 ÷ 5 : Remainder = 0
800 ÷ 5 : Remainder = 0
12500 ÷ 10 : Remainder = 0
800 ÷ 8 : Remainder = 0
12500 ÷ 20 : Remainder = 0
800 ÷ 10 : Remainder = 0
12500 ÷ 25 : Remainder = 0
800 ÷ 16 : Remainder = 0
12500 ÷ 50 : Remainder = 0
800 ÷ 20 : Remainder = 0
12500 ÷ 100 : Remainder = 0
800 ÷ 25 : Remainder = 0
12500 ÷ 125 : Remainder = 0
800 ÷ 32 : Remainder = 0
12500 ÷ 250 : Remainder = 0
800 ÷ 40 : Remainder = 0
12500 ÷ 500 : Remainder = 0
800 ÷ 50 : Remainder = 0
12500 ÷ 625 : Remainder = 0
800 ÷ 80 : Remainder = 0
12500 ÷ 1250 : Remainder = 0
800 ÷ 100 : Remainder = 0
12500 ÷ 2500 : Remainder = 0
800 ÷ 160 : Remainder = 0
12500 ÷ 3125 : Remainder = 0
800 ÷ 200 : Remainder = 0
12500 ÷ 6250 : Remainder = 0
800 ÷ 400 : Remainder = 0
12500 ÷ 12500 : Remainder = 0
800 ÷ 800 : Remainder = 0
Hence, Factors of
12500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500, 3125, 6250, and 12500
And, Factors of
800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800
Examples of GCF
Sammy baked 12500 chocolate cookies and 800 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 12500 and 800.
GCF of 12500 and 800 is 100.
A class has 12500 boys and 800 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 12500 and 800. Hence, GCF of 12500 and 800 is 100.
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.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(12500, 800) = ( 12500 * 800 ) / LCM(12500, 800) = 100.
What is the GCF of 12500 and 800?GCF of 12500 and 800 is 100.
Ariel is making ready to eat meals to share with friends. She has 12500 bottles of water and 800 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 12500 and 800. So the GCF of 12500 and 800 is 100.
Mary has 12500 blue buttons and 800 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 12500 and 800. Hence, the GCF of 12500 and 800 or the greatest arrangement is 100.
Kamal is making identical balloon arrangements for a party. He has 12500 maroon balloons, and 800 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 12500 and 800. So the GCF of 12500 and 800 is 100.
Kunal is making baskets full of nuts and dried fruits. He has 12500 bags of nuts and 800 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 12500 and 800. So the GCF of 12500 and 800 is 100.
A class has 12500 boys and 800 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 12500 and 800. Hence, GCF of 12500 and 800 is 100.