How do you explain GCF in mathematics?
GCF or greatest common factor of two or more numbers is defined as largest possible number or integer which is the factor of all given number or in other words we can say that largest possible common number which completely divides the given numbers. GCF of two numbers can be represented as GCF (144, 240).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 144 and 240 is 48, where 48 is less than both 144 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.
How can we define factors?
In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.
Properties of Factors
- Each number is a factor of itself. Eg. 144 and 240 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 144 and also of 240.
- Every number is a factor of zero (0), since 144 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, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 are exact divisors of 144 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 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Each factor divides 144 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, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 are all less than or equal to 144 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 144 and 240
- Step 1. Find all the numbers that would divide 144 and 240 without leaving any remainder. Starting with the number 1 upto 72 (half of 144) and 1 upto 120 (half of 240). The number 1 and the number itself are always factors of the given number.
144 ÷ 1 : Remainder = 0
240 ÷ 1 : Remainder = 0
144 ÷ 2 : Remainder = 0
240 ÷ 2 : Remainder = 0
144 ÷ 3 : Remainder = 0
240 ÷ 3 : Remainder = 0
144 ÷ 4 : Remainder = 0
240 ÷ 4 : Remainder = 0
144 ÷ 6 : Remainder = 0
240 ÷ 5 : Remainder = 0
144 ÷ 8 : Remainder = 0
240 ÷ 6 : Remainder = 0
144 ÷ 9 : Remainder = 0
240 ÷ 8 : Remainder = 0
144 ÷ 12 : Remainder = 0
240 ÷ 10 : Remainder = 0
144 ÷ 16 : Remainder = 0
240 ÷ 12 : Remainder = 0
144 ÷ 18 : Remainder = 0
240 ÷ 15 : Remainder = 0
144 ÷ 24 : Remainder = 0
240 ÷ 16 : Remainder = 0
144 ÷ 36 : Remainder = 0
240 ÷ 20 : Remainder = 0
144 ÷ 48 : Remainder = 0
240 ÷ 24 : Remainder = 0
144 ÷ 72 : Remainder = 0
240 ÷ 30 : Remainder = 0
144 ÷ 144 : Remainder = 0
240 ÷ 40 : Remainder = 0
240 ÷ 120 : Remainder = 0
240 ÷ 240 : Remainder = 0
Hence, Factors of
144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144
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
Sammy baked 144 chocolate cookies and 240 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 144 and 240.
GCF of 144 and 240 is 48.
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(144, 240) = ( 144 * 240 ) / LCM(144, 240) = 48.
What is the GCF of 144 and 240?GCF of 144 and 240 is 48.
Ram has 144 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 144 and 240. Hence GCF of 144 and 240 is 48. So the number of tables that can be arranged is 48.
Rubel is creating individual servings of starters for her birthday party. He has 144 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 144 and 240. Thus GCF of 144 and 240 is 48.
Ariel is making ready to eat meals to share with friends. She has 144 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 144 and 240. So the GCF of 144 and 240 is 48.
Mary has 144 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 144 and 240. Hence, the GCF of 144 and 240 or the greatest arrangement is 48.
Kamal is making identical balloon arrangements for a party. He has 144 maroon balloons, and 240 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 144 and 240. So the GCF of 144 and 240 is 48.