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 (225, 360).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 225 and 360 is 45, where 45 is less than both the numbers.
- If the given numbers are consecutive than GCF is always 1.
- Product of two numbers is always equal to the product of their GCF and LCM.
- 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
- Every factor of a number is an exact divisor of that number, example 1, 3, 5, 9, 15, 25, 45, 75, 225 are exact divisors of 225 and 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 are exact divisors of 360.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 225 and 360 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 225 and also of 360.
Steps to find Factors of 225 and 360
- Step 1. Find all the numbers that would divide 225 and 360 without leaving any remainder. Starting with the number 1 upto 112 (half of 225) and 1 upto 180 (half of 360). The number 1 and the number itself are always factors of the given number.
225 ÷ 1 : Remainder = 0
360 ÷ 1 : Remainder = 0
225 ÷ 3 : Remainder = 0
360 ÷ 2 : Remainder = 0
225 ÷ 5 : Remainder = 0
360 ÷ 3 : Remainder = 0
225 ÷ 9 : Remainder = 0
360 ÷ 4 : Remainder = 0
225 ÷ 15 : Remainder = 0
360 ÷ 5 : Remainder = 0
225 ÷ 25 : Remainder = 0
360 ÷ 6 : Remainder = 0
225 ÷ 45 : Remainder = 0
360 ÷ 8 : Remainder = 0
225 ÷ 75 : Remainder = 0
360 ÷ 9 : Remainder = 0
225 ÷ 225 : Remainder = 0
360 ÷ 10 : Remainder = 0
360 ÷ 120 : Remainder = 0
360 ÷ 180 : Remainder = 0
360 ÷ 360 : Remainder = 0
Hence, Factors of
225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225
And, Factors of
360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360
Examples of GCF
Sammy baked 225 chocolate cookies and 360 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 225 and 360.
GCF of 225 and 360 is 45.
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(225, 360) = ( 225 * 360 ) / LCM(225, 360) = 45.
What is the GCF of 225 and 360?GCF of 225 and 360 is 45.
Ram has 225 cans of Pepsi and 360 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 225 and 360. Hence GCF of 225 and 360 is 45. So the number of tables that can be arranged is 45.
Rubel is creating individual servings of starters for her birthday party. He has 225 pizzas and 360 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 225 and 360. Thus GCF of 225 and 360 is 45.
Ariel is making ready to eat meals to share with friends. She has 225 bottles of water and 360 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 225 and 360. So the GCF of 225 and 360 is 45.
Mary has 225 blue buttons and 360 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 225 and 360. Hence, the GCF of 225 and 360 or the greatest arrangement is 45.
Kamal is making identical balloon arrangements for a party. He has 225 maroon balloons, and 360 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 225 and 360. So the GCF of 225 and 360 is 45.