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. 300 and 360 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 300 and also of 360.
- Every number is a factor of zero (0), since 300 x 0 = 0 and 360 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, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300 are exact divisors of 300 and 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 are exact divisors of 360.
- Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. Each factor divides 300 without leaving a remainder.
Simlarly, factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. Each factor divides 360 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300 are all less than or equal to 300 and 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 are all less than or equal to 360.
Steps to find Factors of 300 and 360
- Step 1. Find all the numbers that would divide 300 and 360 without leaving any remainder. Starting with the number 1 upto 150 (half of 300) and 1 upto 180 (half of 360). The number 1 and the number itself are always factors of the given number.
300 ÷ 1 : Remainder = 0
360 ÷ 1 : Remainder = 0
300 ÷ 2 : Remainder = 0
360 ÷ 2 : Remainder = 0
300 ÷ 3 : Remainder = 0
360 ÷ 3 : Remainder = 0
300 ÷ 4 : Remainder = 0
360 ÷ 4 : Remainder = 0
300 ÷ 5 : Remainder = 0
360 ÷ 5 : Remainder = 0
300 ÷ 6 : Remainder = 0
360 ÷ 6 : Remainder = 0
300 ÷ 10 : Remainder = 0
360 ÷ 8 : Remainder = 0
300 ÷ 12 : Remainder = 0
360 ÷ 9 : Remainder = 0
300 ÷ 15 : Remainder = 0
360 ÷ 10 : Remainder = 0
300 ÷ 20 : Remainder = 0
360 ÷ 12 : Remainder = 0
300 ÷ 25 : Remainder = 0
360 ÷ 15 : Remainder = 0
300 ÷ 30 : Remainder = 0
360 ÷ 18 : Remainder = 0
300 ÷ 50 : Remainder = 0
360 ÷ 20 : Remainder = 0
300 ÷ 60 : Remainder = 0
360 ÷ 24 : Remainder = 0
300 ÷ 75 : Remainder = 0
360 ÷ 30 : Remainder = 0
300 ÷ 100 : Remainder = 0
360 ÷ 36 : Remainder = 0
300 ÷ 150 : Remainder = 0
360 ÷ 40 : Remainder = 0
300 ÷ 300 : Remainder = 0
360 ÷ 45 : Remainder = 0
360 ÷ 120 : Remainder = 0
360 ÷ 180 : Remainder = 0
360 ÷ 360 : Remainder = 0
Hence, Factors of
300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300
And, Factors of
360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360
Examples of GCF
Sammy baked 300 chocolate cookies and 360 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 300 and 360.
GCF of 300 and 360 is 60.
A class has 300 boys and 360 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 300 and 360. Hence, GCF of 300 and 360 is 60.
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.
Ram has 300 cans of Pepsi and 360 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 300 and 360. Hence GCF of 300 and 360 is 60. So the number of tables that can be arranged is 60.
Ariel is making ready to eat meals to share with friends. She has 300 bottles of water and 360 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 300 and 360. So the GCF of 300 and 360 is 60.
Mary has 300 blue buttons and 360 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 300 and 360. Hence, the GCF of 300 and 360 or the greatest arrangement is 60.
Kamal is making identical balloon arrangements for a party. He has 300 maroon balloons, and 360 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 300 and 360. So the GCF of 300 and 360 is 60.
Kunal is making baskets full of nuts and dried fruits. He has 300 bags of nuts and 360 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 300 and 360. So the GCF of 300 and 360 is 60.
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 300 bus tickets and 360 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 300 and 360. Hence, GCF of 300 and 360 is 60.