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 (200, 240).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 200 and 240 is 40, where 40 is less than both 200 and 240.
- 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. 200 and 240 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 200 and also of 240.
- Every number is a factor of zero (0), since 200 x 0 = 0 and 240 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, 20, 25, 40, 50, 100, 200 are exact divisors of 200 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 are exact divisors of 240.
- Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. Each factor divides 200 without leaving a remainder.
Simlarly, factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240. Each factor divides 240 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200 are all less than or equal to 200 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 are all less than or equal to 240.
Steps to find Factors of 200 and 240
- Step 1. Find all the numbers that would divide 200 and 240 without leaving any remainder. Starting with the number 1 upto 100 (half of 200) and 1 upto 120 (half of 240). The number 1 and the number itself are always factors of the given number.
200 ÷ 1 : Remainder = 0
240 ÷ 1 : Remainder = 0
200 ÷ 2 : Remainder = 0
240 ÷ 2 : Remainder = 0
200 ÷ 4 : Remainder = 0
240 ÷ 3 : Remainder = 0
200 ÷ 5 : Remainder = 0
240 ÷ 4 : Remainder = 0
200 ÷ 8 : Remainder = 0
240 ÷ 5 : Remainder = 0
200 ÷ 10 : Remainder = 0
240 ÷ 6 : Remainder = 0
200 ÷ 20 : Remainder = 0
240 ÷ 8 : Remainder = 0
200 ÷ 25 : Remainder = 0
240 ÷ 10 : Remainder = 0
200 ÷ 40 : Remainder = 0
240 ÷ 12 : Remainder = 0
200 ÷ 50 : Remainder = 0
240 ÷ 15 : Remainder = 0
200 ÷ 100 : Remainder = 0
240 ÷ 16 : Remainder = 0
200 ÷ 200 : Remainder = 0
240 ÷ 20 : Remainder = 0
240 ÷ 120 : Remainder = 0
240 ÷ 240 : Remainder = 0
Hence, Factors of
200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200
And, Factors of
240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240
Examples of GCF
A class has 200 boys and 240 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 200 and 240. Hence, GCF of 200 and 240 is 40.
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(200, 240) = ( 200 * 240 ) / LCM(200, 240) = 40.
What is the GCF of 200 and 240?GCF of 200 and 240 is 40.
Ram has 200 cans of Pepsi and 240 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 200 and 240. Hence GCF of 200 and 240 is 40. So the number of tables that can be arranged is 40.
Rubel is creating individual servings of starters for her birthday party. He has 200 pizzas and 240 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 200 and 240. Thus GCF of 200 and 240 is 40.
Ariel is making ready to eat meals to share with friends. She has 200 bottles of water and 240 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 200 and 240. So the GCF of 200 and 240 is 40.
Mary has 200 blue buttons and 240 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 200 and 240. Hence, the GCF of 200 and 240 or the greatest arrangement is 40.
Kunal is making baskets full of nuts and dried fruits. He has 200 bags of nuts and 240 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 200 and 240. So the GCF of 200 and 240 is 40.