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. 162 and 189 are factors of themselves respectively.
- 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, 6, 9, 18, 27, 54, 81, 162 are exact divisors of 162 and 1, 3, 7, 9, 21, 27, 63, 189 are exact divisors of 189.
- 1 is a factor of every number. Eg. 1 is a factor of 162 and also of 189.
- Every number is a factor of zero (0), since 162 x 0 = 0 and 189 x 0 = 0.
Steps to find Factors of 162 and 189
- Step 1. Find all the numbers that would divide 162 and 189 without leaving any remainder. Starting with the number 1 upto 81 (half of 162) and 1 upto 94 (half of 189). The number 1 and the number itself are always factors of the given number.
162 ÷ 1 : Remainder = 0
189 ÷ 1 : Remainder = 0
162 ÷ 2 : Remainder = 0
189 ÷ 3 : Remainder = 0
162 ÷ 3 : Remainder = 0
189 ÷ 7 : Remainder = 0
162 ÷ 6 : Remainder = 0
189 ÷ 9 : Remainder = 0
162 ÷ 9 : Remainder = 0
189 ÷ 21 : Remainder = 0
162 ÷ 18 : Remainder = 0
189 ÷ 27 : Remainder = 0
162 ÷ 27 : Remainder = 0
189 ÷ 63 : Remainder = 0
162 ÷ 54 : Remainder = 0
189 ÷ 189 : Remainder = 0
162 ÷ 162 : Remainder = 0
Hence, Factors of
162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162
And, Factors of
189 are 1, 3, 7, 9, 21, 27, 63, and 189
Examples of GCF
Sammy baked 162 chocolate cookies and 189 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 162 and 189.
GCF of 162 and 189 is 27.
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(162, 189) = ( 162 * 189 ) / LCM(162, 189) = 27.
What is the GCF of 162 and 189?GCF of 162 and 189 is 27.
Ram has 162 cans of Pepsi and 189 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 162 and 189. Hence GCF of 162 and 189 is 27. So the number of tables that can be arranged is 27.
Rubel is creating individual servings of starters for her birthday party. He has 162 pizzas and 189 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 162 and 189. Thus GCF of 162 and 189 is 27.
Ariel is making ready to eat meals to share with friends. She has 162 bottles of water and 189 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 162 and 189. So the GCF of 162 and 189 is 27.
Mary has 162 blue buttons and 189 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 162 and 189. Hence, the GCF of 162 and 189 or the greatest arrangement is 27.
Kamal is making identical balloon arrangements for a party. He has 162 maroon balloons, and 189 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 162 and 189. So the GCF of 162 and 189 is 27.