How can we define factors?
In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 36 and 180 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 36 and also of 180.
- Every number is a factor of zero (0), since 36 x 0 = 0 and 180 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, 36 are exact divisors of 36 and 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 are exact divisors of 180.
- Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Each factor divides 36 without leaving a remainder.
Simlarly, 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. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 18, 36 are all less than or equal to 36 and 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.
Steps to find Factors of 36 and 180
- Step 1. Find all the numbers that would divide 36 and 180 without leaving any remainder. Starting with the number 1 upto 18 (half of 36) and 1 upto 90 (half of 180). The number 1 and the number itself are always factors of the given number.
36 ÷ 1 : Remainder = 0
180 ÷ 1 : Remainder = 0
36 ÷ 2 : Remainder = 0
180 ÷ 2 : Remainder = 0
36 ÷ 3 : Remainder = 0
180 ÷ 3 : Remainder = 0
36 ÷ 4 : Remainder = 0
180 ÷ 4 : Remainder = 0
36 ÷ 6 : Remainder = 0
180 ÷ 5 : Remainder = 0
36 ÷ 9 : Remainder = 0
180 ÷ 6 : Remainder = 0
36 ÷ 12 : Remainder = 0
180 ÷ 9 : Remainder = 0
36 ÷ 18 : Remainder = 0
180 ÷ 10 : Remainder = 0
36 ÷ 36 : Remainder = 0
180 ÷ 12 : Remainder = 0
180 ÷ 180 : Remainder = 0
Hence, Factors of
36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36
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 36 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 36 and 180.
GCF of 36 and 180 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(36, 180) = ( 36 * 180 ) / LCM(36, 180) = 36.
What is the GCF of 36 and 180?GCF of 36 and 180 is 36.
Ram has 36 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 36 and 180. Hence GCF of 36 and 180 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 36 pizzas and 180 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 36 and 180. Thus GCF of 36 and 180 is 36.
Ariel is making ready to eat meals to share with friends. She has 36 bottles of water and 180 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 36 and 180. So the GCF of 36 and 180 is 36.
Mary has 36 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 36 and 180. Hence, the GCF of 36 and 180 or the greatest arrangement is 36.
Kamal is making identical balloon arrangements for a party. He has 36 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 36 and 180. So the GCF of 36 and 180 is 36.