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 (189, 220).
Properties of GCF
- The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 189 and 220 is 1, where 1 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.
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
- Every factor of a number is an exact divisor of that number, example 1, 3, 7, 9, 21, 27, 63, 189 are exact divisors of 189 and 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220 are exact divisors of 220.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 189 and 220 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 189 and also of 220.
Steps to find Factors of 189 and 220
- Step 1. Find all the numbers that would divide 189 and 220 without leaving any remainder. Starting with the number 1 upto 94 (half of 189) and 1 upto 110 (half of 220). The number 1 and the number itself are always factors of the given number.
189 ÷ 1 : Remainder = 0
220 ÷ 1 : Remainder = 0
189 ÷ 3 : Remainder = 0
220 ÷ 2 : Remainder = 0
189 ÷ 7 : Remainder = 0
220 ÷ 4 : Remainder = 0
189 ÷ 9 : Remainder = 0
220 ÷ 5 : Remainder = 0
189 ÷ 21 : Remainder = 0
220 ÷ 10 : Remainder = 0
189 ÷ 27 : Remainder = 0
220 ÷ 11 : Remainder = 0
189 ÷ 63 : Remainder = 0
220 ÷ 20 : Remainder = 0
189 ÷ 189 : Remainder = 0
220 ÷ 22 : Remainder = 0
220 ÷ 110 : Remainder = 0
220 ÷ 220 : Remainder = 0
Hence, Factors of
189 are 1, 3, 7, 9, 21, 27, 63, and 189
And, Factors of
220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, and 220
Examples of GCF
Sammy baked 189 chocolate cookies and 220 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 189 and 220.
GCF of 189 and 220 is 1.
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(189, 220) = ( 189 * 220 ) / LCM(189, 220) = 1.
What is the GCF of 189 and 220?GCF of 189 and 220 is 1.
Ram has 189 cans of Pepsi and 220 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 189 and 220. Hence GCF of 189 and 220 is 1. So the number of tables that can be arranged is 1.
Rubel is creating individual servings of starters for her birthday party. He has 189 pizzas and 220 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 189 and 220. Thus GCF of 189 and 220 is 1.
Ariel is making ready to eat meals to share with friends. She has 189 bottles of water and 220 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 189 and 220. So the GCF of 189 and 220 is 1.
Mary has 189 blue buttons and 220 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 189 and 220. Hence, the GCF of 189 and 220 or the greatest arrangement is 1.
Kamal is making identical balloon arrangements for a party. He has 189 maroon balloons, and 220 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 189 and 220. So the GCF of 189 and 220 is 1.