What is the definition of factors?
In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.
Properties of Factors
- Every number is a factor of zero (0), since 243 x 0 = 0 and 324 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, 81, 243 are exact divisors of 243 and 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324 are exact divisors of 324.
- Factors of 243 are 1, 3, 9, 27, 81, 243. Each factor divides 243 without leaving a remainder.
Simlarly, 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.
Steps to find Factors of 243 and 324
- Step 1. Find all the numbers that would divide 243 and 324 without leaving any remainder. Starting with the number 1 upto 121 (half of 243) and 1 upto 162 (half of 324). The number 1 and the number itself are always factors of the given number.
243 ÷ 1 : Remainder = 0
324 ÷ 1 : Remainder = 0
243 ÷ 3 : Remainder = 0
324 ÷ 2 : Remainder = 0
243 ÷ 9 : Remainder = 0
324 ÷ 3 : Remainder = 0
243 ÷ 27 : Remainder = 0
324 ÷ 4 : Remainder = 0
243 ÷ 81 : Remainder = 0
324 ÷ 6 : Remainder = 0
243 ÷ 243 : Remainder = 0
324 ÷ 9 : Remainder = 0
324 ÷ 108 : Remainder = 0
324 ÷ 162 : Remainder = 0
324 ÷ 324 : Remainder = 0
Hence, Factors of
243 are 1, 3, 9, 27, 81, and 243
And, Factors of
324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324
Examples of GCF
Sammy baked 243 chocolate cookies and 324 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 243 and 324.
GCF of 243 and 324 is 81.
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(243, 324) = ( 243 * 324 ) / LCM(243, 324) = 81.
What is the GCF of 243 and 324?GCF of 243 and 324 is 81.
Ram has 243 cans of Pepsi and 324 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 243 and 324. Hence GCF of 243 and 324 is 81. So the number of tables that can be arranged is 81.
Rubel is creating individual servings of starters for her birthday party. He has 243 pizzas and 324 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 243 and 324. Thus GCF of 243 and 324 is 81.
Ariel is making ready to eat meals to share with friends. She has 243 bottles of water and 324 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 243 and 324. So the GCF of 243 and 324 is 81.
Mary has 243 blue buttons and 324 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 243 and 324. Hence, the GCF of 243 and 324 or the greatest arrangement is 81.
Kamal is making identical balloon arrangements for a party. He has 243 maroon balloons, and 324 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 243 and 324. So the GCF of 243 and 324 is 81.