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 (10, 180).
Properties of GCF
- Given two numbers 10 and 180, such that GCF is 10 where 10 will always be less than 10 and 180.
- 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.
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. 10 and 180 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, 5, 10 are exact divisors of 10 and 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 are exact divisors of 180.
- 1 is a factor of every number. Eg. 1 is a factor of 10 and also of 180.
- Every number is a factor of zero (0), since 10 x 0 = 0 and 180 x 0 = 0.
Steps to find Factors of 10 and 180
- Step 1. Find all the numbers that would divide 10 and 180 without leaving any remainder. Starting with the number 1 upto 5 (half of 10) and 1 upto 90 (half of 180). The number 1 and the number itself are always factors of the given number.
10 ÷ 1 : Remainder = 0
180 ÷ 1 : Remainder = 0
10 ÷ 2 : Remainder = 0
180 ÷ 2 : Remainder = 0
10 ÷ 5 : Remainder = 0
180 ÷ 3 : Remainder = 0
10 ÷ 10 : Remainder = 0
180 ÷ 4 : Remainder = 0
180 ÷ 180 : Remainder = 0
Hence, Factors of
10 are 1, 2, 5, and 10
And, Factors of
180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180
Examples of GCF
Sammy baked 10 chocolate cookies and 180 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 10 and 180.
GCF of 10 and 180 is 10.
A class has 10 boys and 180 girls. A choir teacher wants to form a choir team from this class such that the students are standing in equal rows also girls or boys will be in each row. Teacher wants to know the greatest number of students that could be in each row, can you help him?To find the greatest number of students that could be in each row, we need to find the GCF of 10 and 180. Hence, GCF of 10 and 180 is 10.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(10, 180) = ( 10 * 180 ) / LCM(10, 180) = 10.
What is the GCF of 10 and 180?GCF of 10 and 180 is 10.
Ram has 10 cans of Pepsi and 180 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 10 and 180. Hence GCF of 10 and 180 is 10. So the number of tables that can be arranged is 10.
Mary has 10 blue buttons and 180 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 10 and 180. Hence, the GCF of 10 and 180 or the greatest arrangement is 10.
Kamal is making identical balloon arrangements for a party. He has 10 maroon balloons, and 180 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 10 and 180. So the GCF of 10 and 180 is 10.
Kunal is making baskets full of nuts and dried fruits. He has 10 bags of nuts and 180 bags of dried fruits. He wants each basket to be identical, containing the same combination of bags of nuts and bags of driesn fruits, with no left overs. What is the greatest number of baskets that Kunal can make?the greatest number of baskets that Kunal can make would be equal to GCF of 10 and 180. So the GCF of 10 and 180 is 10.
To energize public transportation, Abir needs to give a few companions envelopes with transport tickets, and metro tickets in them. On the off chance that he has 10 bus tickets and 180 metro tickets to be parted similarly among the envelopes, and he need no tickets left. What is the greatest number of envelopes Abir can make?To make the greatest number of envelopes Abir needs to find out the GCF of 10 and 180. Hence, GCF of 10 and 180 is 10.