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 (180, 378).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 180 and 378 is 18, where 18 is less than both 180 and 378.
- 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. 180 and 378 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 180 and also of 378.
- Every number is a factor of zero (0), since 180 x 0 = 0 and 378 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, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 are exact divisors of 180 and 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378 are exact divisors of 378.
- Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. Each factor divides 180 without leaving a remainder.
Simlarly, factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378. Each factor divides 378 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 are all less than or equal to 180 and 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378 are all less than or equal to 378.
Steps to find Factors of 180 and 378
- Step 1. Find all the numbers that would divide 180 and 378 without leaving any remainder. Starting with the number 1 upto 90 (half of 180) and 1 upto 189 (half of 378). The number 1 and the number itself are always factors of the given number.
180 ÷ 1 : Remainder = 0
378 ÷ 1 : Remainder = 0
180 ÷ 2 : Remainder = 0
378 ÷ 2 : Remainder = 0
180 ÷ 3 : Remainder = 0
378 ÷ 3 : Remainder = 0
180 ÷ 4 : Remainder = 0
378 ÷ 6 : Remainder = 0
180 ÷ 5 : Remainder = 0
378 ÷ 7 : Remainder = 0
180 ÷ 6 : Remainder = 0
378 ÷ 9 : Remainder = 0
180 ÷ 9 : Remainder = 0
378 ÷ 14 : Remainder = 0
180 ÷ 10 : Remainder = 0
378 ÷ 18 : Remainder = 0
180 ÷ 12 : Remainder = 0
378 ÷ 21 : Remainder = 0
180 ÷ 15 : Remainder = 0
378 ÷ 27 : Remainder = 0
180 ÷ 18 : Remainder = 0
378 ÷ 42 : Remainder = 0
180 ÷ 20 : Remainder = 0
378 ÷ 54 : Remainder = 0
180 ÷ 30 : Remainder = 0
378 ÷ 63 : Remainder = 0
180 ÷ 36 : Remainder = 0
378 ÷ 126 : Remainder = 0
180 ÷ 45 : Remainder = 0
378 ÷ 189 : Remainder = 0
180 ÷ 60 : Remainder = 0
378 ÷ 378 : Remainder = 0
180 ÷ 180 : Remainder = 0
Hence, Factors of
180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180
And, Factors of
378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, and 378
Examples of GCF
Sammy baked 180 chocolate cookies and 378 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 180 and 378.
GCF of 180 and 378 is 18.
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(180, 378) = ( 180 * 378 ) / LCM(180, 378) = 18.
What is the GCF of 180 and 378?GCF of 180 and 378 is 18.
Ram has 180 cans of Pepsi and 378 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 180 and 378. Hence GCF of 180 and 378 is 18. So the number of tables that can be arranged is 18.
Rubel is creating individual servings of starters for her birthday party. He has 180 pizzas and 378 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 180 and 378. Thus GCF of 180 and 378 is 18.
Ariel is making ready to eat meals to share with friends. She has 180 bottles of water and 378 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 180 and 378. So the GCF of 180 and 378 is 18.
Mary has 180 blue buttons and 378 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 180 and 378. Hence, the GCF of 180 and 378 or the greatest arrangement is 18.
Kamal is making identical balloon arrangements for a party. He has 180 maroon balloons, and 378 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 180 and 378. So the GCF of 180 and 378 is 18.