How do you explain factors?
In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.
Properties of Factors
- Every number is a factor of zero (0), since 27 x 0 = 0 and 36 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, 3, 9, 27 are exact divisors of 27 and 1, 2, 3, 4, 6, 9, 12, 18, 36 are exact divisors of 36.
- Factors of 27 are 1, 3, 9, 27. Each factor divides 27 without leaving a remainder.
Simlarly, factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Each factor divides 36 without leaving a remainder.
Steps to find Factors of 27 and 36
- Step 1. Find all the numbers that would divide 27 and 36 without leaving any remainder. Starting with the number 1 upto 13 (half of 27) and 1 upto 18 (half of 36). The number 1 and the number itself are always factors of the given number.
27 ÷ 1 : Remainder = 0
36 ÷ 1 : Remainder = 0
27 ÷ 3 : Remainder = 0
36 ÷ 2 : Remainder = 0
27 ÷ 9 : Remainder = 0
36 ÷ 3 : Remainder = 0
27 ÷ 27 : Remainder = 0
36 ÷ 4 : Remainder = 0
Hence, Factors of
27 are 1, 3, 9, and 27
And, Factors of
36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36
Examples of GCF
Sammy baked 27 chocolate cookies and 36 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 27 and 36.
GCF of 27 and 36 is 9.
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(27, 36) = ( 27 * 36 ) / LCM(27, 36) = 9.
What is the GCF of 27 and 36?
GCF of 27 and 36 is 9.
Ram has 27 cans of Pepsi and 36 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 27 and 36. Hence GCF of 27 and 36 is 9. So the number of tables that can be arranged is 9.
Rubel is creating individual servings of starters for her birthday party. He has 27 pizzas and 36 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 27 and 36. Thus GCF of 27 and 36 is 9.
Ariel is making ready to eat meals to share with friends. She has 27 bottles of water and 36 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 27 and 36. So the GCF of 27 and 36 is 9.
Mary has 27 blue buttons and 36 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 27 and 36. Hence, the GCF of 27 and 36 or the greatest arrangement is 9.
Kamal is making identical balloon arrangements for a party. He has 27 maroon balloons, and 36 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 27 and 36. So the GCF of 27 and 36 is 9.