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 (54, 60).
Properties of GCF
- Given two numbers 54 and 60, such that GCF is 6 where 6 will always be less than 54 and 60.
- GCF of two numbers is always equal to 1 in case given numbers are consecutive.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- The GCF of two given numbers is either 1 or the number itself if one of them is a prime number.
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. 54 and 60 are factors of themselves respectively.
- 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, 6, 9, 18, 27, 54 are exact divisors of 54 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 are exact divisors of 60.
- 1 is a factor of every number. Eg. 1 is a factor of 54 and also of 60.
- Every number is a factor of zero (0), since 54 x 0 = 0 and 60 x 0 = 0.
Steps to find Factors of 54 and 60
- Step 1. Find all the numbers that would divide 54 and 60 without leaving any remainder. Starting with the number 1 upto 27 (half of 54) and 1 upto 30 (half of 60). The number 1 and the number itself are always factors of the given number.
54 ÷ 1 : Remainder = 0
60 ÷ 1 : Remainder = 0
54 ÷ 2 : Remainder = 0
60 ÷ 2 : Remainder = 0
54 ÷ 3 : Remainder = 0
60 ÷ 3 : Remainder = 0
54 ÷ 6 : Remainder = 0
60 ÷ 4 : Remainder = 0
54 ÷ 9 : Remainder = 0
60 ÷ 5 : Remainder = 0
54 ÷ 18 : Remainder = 0
60 ÷ 6 : Remainder = 0
54 ÷ 27 : Remainder = 0
60 ÷ 10 : Remainder = 0
54 ÷ 54 : Remainder = 0
60 ÷ 12 : Remainder = 0
Hence, Factors of
54 are 1, 2, 3, 6, 9, 18, 27, and 54
And, Factors of
60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
Examples of GCF
Sammy baked 54 chocolate cookies and 60 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 54 and 60.
GCF of 54 and 60 is 6.
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(54, 60) = ( 54 * 60 ) / LCM(54, 60) = 6.
What is the GCF of 54 and 60?GCF of 54 and 60 is 6.
Ram has 54 cans of Pepsi and 60 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 54 and 60. Hence GCF of 54 and 60 is 6. So the number of tables that can be arranged is 6.
Rubel is creating individual servings of starters for her birthday party. He has 54 pizzas and 60 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 54 and 60. Thus GCF of 54 and 60 is 6.
Ariel is making ready to eat meals to share with friends. She has 54 bottles of water and 60 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 54 and 60. So the GCF of 54 and 60 is 6.
Mary has 54 blue buttons and 60 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 54 and 60. Hence, the GCF of 54 and 60 or the greatest arrangement is 6.
Kamal is making identical balloon arrangements for a party. He has 54 maroon balloons, and 60 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 54 and 60. So the GCF of 54 and 60 is 6.