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. 324 and 360 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 324 and also of 360.
- Every number is a factor of zero (0), since 324 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, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324 are exact divisors of 324 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 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324. Each factor divides 324 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, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324 are all less than or equal to 324 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 324 and 360
- Step 1. Find all the numbers that would divide 324 and 360 without leaving any remainder. Starting with the number 1 upto 162 (half of 324) and 1 upto 180 (half of 360). The number 1 and the number itself are always factors of the given number.
324 ÷ 1 : Remainder = 0
360 ÷ 1 : Remainder = 0
324 ÷ 2 : Remainder = 0
360 ÷ 2 : Remainder = 0
324 ÷ 3 : Remainder = 0
360 ÷ 3 : Remainder = 0
324 ÷ 4 : Remainder = 0
360 ÷ 4 : Remainder = 0
324 ÷ 6 : Remainder = 0
360 ÷ 5 : Remainder = 0
324 ÷ 9 : Remainder = 0
360 ÷ 6 : Remainder = 0
324 ÷ 12 : Remainder = 0
360 ÷ 8 : Remainder = 0
324 ÷ 18 : Remainder = 0
360 ÷ 9 : Remainder = 0
324 ÷ 27 : Remainder = 0
360 ÷ 10 : Remainder = 0
324 ÷ 36 : Remainder = 0
360 ÷ 12 : Remainder = 0
324 ÷ 54 : Remainder = 0
360 ÷ 15 : Remainder = 0
324 ÷ 81 : Remainder = 0
360 ÷ 18 : Remainder = 0
324 ÷ 108 : Remainder = 0
360 ÷ 20 : Remainder = 0
324 ÷ 162 : Remainder = 0
360 ÷ 24 : Remainder = 0
324 ÷ 324 : Remainder = 0
360 ÷ 30 : Remainder = 0
360 ÷ 120 : Remainder = 0
360 ÷ 180 : Remainder = 0
360 ÷ 360 : Remainder = 0
Hence, Factors of
324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324
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 324 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 324 and 360.
GCF of 324 and 360 is 36.
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(324, 360) = ( 324 * 360 ) / LCM(324, 360) = 36.
What is the GCF of 324 and 360?GCF of 324 and 360 is 36.
Ram has 324 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 324 and 360. Hence GCF of 324 and 360 is 36. So the number of tables that can be arranged is 36.
Rubel is creating individual servings of starters for her birthday party. He has 324 pizzas and 360 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 324 and 360. Thus GCF of 324 and 360 is 36.
Ariel is making ready to eat meals to share with friends. She has 324 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 324 and 360. So the GCF of 324 and 360 is 36.
Mary has 324 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 324 and 360. Hence, the GCF of 324 and 360 or the greatest arrangement is 36.
Kamal is making identical balloon arrangements for a party. He has 324 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 324 and 360. So the GCF of 324 and 360 is 36.