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
- Each number is a factor of itself. Eg. 108 and 168 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 108 and also of 168.
- Every number is a factor of zero (0), since 108 x 0 = 0 and 168 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, 27, 36, 54, 108 are exact divisors of 108 and 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 are exact divisors of 168.
- Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. Each factor divides 108 without leaving a remainder.
Simlarly, factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. Each factor divides 168 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, 27, 36, 54, 108 are all less than or equal to 108 and 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 are all less than or equal to 168.
Steps to find Factors of 108 and 168
- Step 1. Find all the numbers that would divide 108 and 168 without leaving any remainder. Starting with the number 1 upto 54 (half of 108) and 1 upto 84 (half of 168). The number 1 and the number itself are always factors of the given number.
108 ÷ 1 : Remainder = 0
168 ÷ 1 : Remainder = 0
108 ÷ 2 : Remainder = 0
168 ÷ 2 : Remainder = 0
108 ÷ 3 : Remainder = 0
168 ÷ 3 : Remainder = 0
108 ÷ 4 : Remainder = 0
168 ÷ 4 : Remainder = 0
108 ÷ 6 : Remainder = 0
168 ÷ 6 : Remainder = 0
108 ÷ 9 : Remainder = 0
168 ÷ 7 : Remainder = 0
108 ÷ 12 : Remainder = 0
168 ÷ 8 : Remainder = 0
108 ÷ 18 : Remainder = 0
168 ÷ 12 : Remainder = 0
108 ÷ 27 : Remainder = 0
168 ÷ 14 : Remainder = 0
108 ÷ 36 : Remainder = 0
168 ÷ 21 : Remainder = 0
108 ÷ 54 : Remainder = 0
168 ÷ 24 : Remainder = 0
108 ÷ 108 : Remainder = 0
168 ÷ 28 : Remainder = 0
168 ÷ 168 : Remainder = 0
Hence, Factors of
108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108
And, Factors of
168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168
Examples of GCF
Sammy baked 108 chocolate cookies and 168 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 108 and 168.
GCF of 108 and 168 is 12.
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(108, 168) = ( 108 * 168 ) / LCM(108, 168) = 12.
What is the GCF of 108 and 168?GCF of 108 and 168 is 12.
Ram has 108 cans of Pepsi and 168 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 108 and 168. Hence GCF of 108 and 168 is 12. So the number of tables that can be arranged is 12.
Rubel is creating individual servings of starters for her birthday party. He has 108 pizzas and 168 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 108 and 168. Thus GCF of 108 and 168 is 12.
Ariel is making ready to eat meals to share with friends. She has 108 bottles of water and 168 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 108 and 168. So the GCF of 108 and 168 is 12.
Mary has 108 blue buttons and 168 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 108 and 168. Hence, the GCF of 108 and 168 or the greatest arrangement is 12.
Kamal is making identical balloon arrangements for a party. He has 108 maroon balloons, and 168 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 108 and 168. So the GCF of 108 and 168 is 12.