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 (2000, 150).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 2000 and 150 is 50, where 50 is less than both 2000 and 150.
- 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. 2000 and 150 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 2000 and also of 150.
- Every number is a factor of zero (0), since 2000 x 0 = 0 and 150 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, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000 are exact divisors of 2000 and 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 are exact divisors of 150.
- Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000. Each factor divides 2000 without leaving a remainder.
Simlarly, factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150. Each factor divides 150 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000 are all less than or equal to 2000 and 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 are all less than or equal to 150.
Steps to find Factors of 2000 and 150
- Step 1. Find all the numbers that would divide 2000 and 150 without leaving any remainder. Starting with the number 1 upto 1000 (half of 2000) and 1 upto 75 (half of 150). The number 1 and the number itself are always factors of the given number.
2000 ÷ 1 : Remainder = 0
150 ÷ 1 : Remainder = 0
2000 ÷ 2 : Remainder = 0
150 ÷ 2 : Remainder = 0
2000 ÷ 4 : Remainder = 0
150 ÷ 3 : Remainder = 0
2000 ÷ 5 : Remainder = 0
150 ÷ 5 : Remainder = 0
2000 ÷ 8 : Remainder = 0
150 ÷ 6 : Remainder = 0
2000 ÷ 10 : Remainder = 0
150 ÷ 10 : Remainder = 0
2000 ÷ 16 : Remainder = 0
150 ÷ 15 : Remainder = 0
2000 ÷ 20 : Remainder = 0
150 ÷ 25 : Remainder = 0
2000 ÷ 25 : Remainder = 0
150 ÷ 30 : Remainder = 0
2000 ÷ 40 : Remainder = 0
150 ÷ 50 : Remainder = 0
2000 ÷ 50 : Remainder = 0
150 ÷ 75 : Remainder = 0
2000 ÷ 80 : Remainder = 0
150 ÷ 150 : Remainder = 0
2000 ÷ 100 : Remainder = 0
2000 ÷ 125 : Remainder = 0
2000 ÷ 200 : Remainder = 0
2000 ÷ 250 : Remainder = 0
2000 ÷ 400 : Remainder = 0
2000 ÷ 500 : Remainder = 0
2000 ÷ 1000 : Remainder = 0
2000 ÷ 2000 : Remainder = 0
Hence, Factors of
2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, and 2000
And, Factors of
150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150
Examples of GCF
A class has 2000 boys and 150 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 2000 and 150. Hence, GCF of 2000 and 150 is 50.
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(2000, 150) = ( 2000 * 150 ) / LCM(2000, 150) = 50.
What is the GCF of 2000 and 150?GCF of 2000 and 150 is 50.
Ram has 2000 cans of Pepsi and 150 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 2000 and 150. Hence GCF of 2000 and 150 is 50. So the number of tables that can be arranged is 50.
Rubel is creating individual servings of starters for her birthday party. He has 2000 pizzas and 150 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 2000 and 150. Thus GCF of 2000 and 150 is 50.
Ariel is making ready to eat meals to share with friends. She has 2000 bottles of water and 150 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 2000 and 150. So the GCF of 2000 and 150 is 50.
Mary has 2000 blue buttons and 150 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 2000 and 150. Hence, the GCF of 2000 and 150 or the greatest arrangement is 50.
Kunal is making baskets full of nuts and dried fruits. He has 2000 bags of nuts and 150 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 2000 and 150. So the GCF of 2000 and 150 is 50.