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
- Each number is a factor of itself. Eg. 432 and 648 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 432 and also of 648.
- Every number is a factor of zero (0), since 432 x 0 = 0 and 648 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, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432 are exact divisors of 432 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648 are exact divisors of 648.
- Factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432. Each factor divides 432 without leaving a remainder.
Simlarly, factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648. Each factor divides 648 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432 are all less than or equal to 432 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648 are all less than or equal to 648.
Steps to find Factors of 432 and 648
- Step 1. Find all the numbers that would divide 432 and 648 without leaving any remainder. Starting with the number 1 upto 216 (half of 432) and 1 upto 324 (half of 648). The number 1 and the number itself are always factors of the given number.
432 ÷ 1 : Remainder = 0
648 ÷ 1 : Remainder = 0
432 ÷ 2 : Remainder = 0
648 ÷ 2 : Remainder = 0
432 ÷ 3 : Remainder = 0
648 ÷ 3 : Remainder = 0
432 ÷ 4 : Remainder = 0
648 ÷ 4 : Remainder = 0
432 ÷ 6 : Remainder = 0
648 ÷ 6 : Remainder = 0
432 ÷ 8 : Remainder = 0
648 ÷ 8 : Remainder = 0
432 ÷ 9 : Remainder = 0
648 ÷ 9 : Remainder = 0
432 ÷ 12 : Remainder = 0
648 ÷ 12 : Remainder = 0
432 ÷ 16 : Remainder = 0
648 ÷ 18 : Remainder = 0
432 ÷ 18 : Remainder = 0
648 ÷ 24 : Remainder = 0
432 ÷ 24 : Remainder = 0
648 ÷ 27 : Remainder = 0
432 ÷ 27 : Remainder = 0
648 ÷ 36 : Remainder = 0
432 ÷ 36 : Remainder = 0
648 ÷ 54 : Remainder = 0
432 ÷ 48 : Remainder = 0
648 ÷ 72 : Remainder = 0
432 ÷ 54 : Remainder = 0
648 ÷ 81 : Remainder = 0
432 ÷ 72 : Remainder = 0
648 ÷ 108 : Remainder = 0
432 ÷ 108 : Remainder = 0
648 ÷ 162 : Remainder = 0
432 ÷ 144 : Remainder = 0
648 ÷ 216 : Remainder = 0
432 ÷ 216 : Remainder = 0
648 ÷ 324 : Remainder = 0
432 ÷ 432 : Remainder = 0
648 ÷ 648 : Remainder = 0
Hence, Factors of
432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, and 432
And, Factors of
648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648
Examples of GCF
Sammy baked 432 chocolate cookies and 648 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 432 and 648.
GCF of 432 and 648 is 216.
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(432, 648) = ( 432 * 648 ) / LCM(432, 648) = 216.
What is the GCF of 432 and 648?GCF of 432 and 648 is 216.
Ram has 432 cans of Pepsi and 648 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 432 and 648. Hence GCF of 432 and 648 is 216. So the number of tables that can be arranged is 216.
Rubel is creating individual servings of starters for her birthday party. He has 432 pizzas and 648 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 432 and 648. Thus GCF of 432 and 648 is 216.
Ariel is making ready to eat meals to share with friends. She has 432 bottles of water and 648 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 432 and 648. So the GCF of 432 and 648 is 216.
Mary has 432 blue buttons and 648 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 432 and 648. Hence, the GCF of 432 and 648 or the greatest arrangement is 216.
Kamal is making identical balloon arrangements for a party. He has 432 maroon balloons, and 648 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 432 and 648. So the GCF of 432 and 648 is 216.