How can we define factors?
In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 156 and 208 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 156 and also of 208.
- Every number is a factor of zero (0), since 156 x 0 = 0 and 208 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, 12, 13, 26, 39, 52, 78, 156 are exact divisors of 156 and 1, 2, 4, 8, 13, 16, 26, 52, 104, 208 are exact divisors of 208.
- Factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156. Each factor divides 156 without leaving a remainder.
Simlarly, factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. Each factor divides 208 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156 are all less than or equal to 156 and 1, 2, 4, 8, 13, 16, 26, 52, 104, 208 are all less than or equal to 208.
Steps to find Factors of 156 and 208
- Step 1. Find all the numbers that would divide 156 and 208 without leaving any remainder. Starting with the number 1 upto 78 (half of 156) and 1 upto 104 (half of 208). The number 1 and the number itself are always factors of the given number.
156 ÷ 1 : Remainder = 0
208 ÷ 1 : Remainder = 0
156 ÷ 2 : Remainder = 0
208 ÷ 2 : Remainder = 0
156 ÷ 3 : Remainder = 0
208 ÷ 4 : Remainder = 0
156 ÷ 4 : Remainder = 0
208 ÷ 8 : Remainder = 0
156 ÷ 6 : Remainder = 0
208 ÷ 13 : Remainder = 0
156 ÷ 12 : Remainder = 0
208 ÷ 16 : Remainder = 0
156 ÷ 13 : Remainder = 0
208 ÷ 26 : Remainder = 0
156 ÷ 26 : Remainder = 0
208 ÷ 52 : Remainder = 0
156 ÷ 39 : Remainder = 0
208 ÷ 104 : Remainder = 0
156 ÷ 52 : Remainder = 0
208 ÷ 208 : Remainder = 0
156 ÷ 156 : Remainder = 0
Hence, Factors of
156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156
And, Factors of
208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, and 208
Examples of GCF
Sammy baked 156 chocolate cookies and 208 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 156 and 208.
GCF of 156 and 208 is 52.
A class has 156 boys and 208 girls. A choir teacher wants to form a choir team from this class such that the students are standing in equal rows also girls or boys will be in each row. Teacher wants to know the greatest number of students that could be in each row, can you help him?To find the greatest number of students that could be in each row, we need to find the GCF of 156 and 208. Hence, GCF of 156 and 208 is 52.
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.
Ram has 156 cans of Pepsi and 208 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 156 and 208. Hence GCF of 156 and 208 is 52. So the number of tables that can be arranged is 52.
Ariel is making ready to eat meals to share with friends. She has 156 bottles of water and 208 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 156 and 208. So the GCF of 156 and 208 is 52.
Mary has 156 blue buttons and 208 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 156 and 208. Hence, the GCF of 156 and 208 or the greatest arrangement is 52.
Kamal is making identical balloon arrangements for a party. He has 156 maroon balloons, and 208 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 156 and 208. So the GCF of 156 and 208 is 52.
Kunal is making baskets full of nuts and dried fruits. He has 156 bags of nuts and 208 bags of dried fruits. He wants each basket to be identical, containing the same combination of bags of nuts and bags of driesn fruits, with no left overs. What is the greatest number of baskets that Kunal can make?the greatest number of baskets that Kunal can make would be equal to GCF of 156 and 208. So the GCF of 156 and 208 is 52.
To energize public transportation, Abir needs to give a few companions envelopes with transport tickets, and metro tickets in them. On the off chance that he has 156 bus tickets and 208 metro tickets to be parted similarly among the envelopes, and he need no tickets left. What is the greatest number of envelopes Abir can make?To make the greatest number of envelopes Abir needs to find out the GCF of 156 and 208. Hence, GCF of 156 and 208 is 52.