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. 136 and 162 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 136 and also of 162.
- Every number is a factor of zero (0), since 136 x 0 = 0 and 162 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, 4, 8, 17, 34, 68, 136 are exact divisors of 136 and 1, 2, 3, 6, 9, 18, 27, 54, 81, 162 are exact divisors of 162.
- Factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136. Each factor divides 136 without leaving a remainder.
Simlarly, factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162. Each factor divides 162 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 17, 34, 68, 136 are all less than or equal to 136 and 1, 2, 3, 6, 9, 18, 27, 54, 81, 162 are all less than or equal to 162.
Steps to find Factors of 136 and 162
- Step 1. Find all the numbers that would divide 136 and 162 without leaving any remainder. Starting with the number 1 upto 68 (half of 136) and 1 upto 81 (half of 162). The number 1 and the number itself are always factors of the given number.
136 ÷ 1 : Remainder = 0
162 ÷ 1 : Remainder = 0
136 ÷ 2 : Remainder = 0
162 ÷ 2 : Remainder = 0
136 ÷ 4 : Remainder = 0
162 ÷ 3 : Remainder = 0
136 ÷ 8 : Remainder = 0
162 ÷ 6 : Remainder = 0
136 ÷ 17 : Remainder = 0
162 ÷ 9 : Remainder = 0
136 ÷ 34 : Remainder = 0
162 ÷ 18 : Remainder = 0
136 ÷ 68 : Remainder = 0
162 ÷ 27 : Remainder = 0
136 ÷ 136 : Remainder = 0
162 ÷ 54 : Remainder = 0
162 ÷ 162 : Remainder = 0
Hence, Factors of
136 are 1, 2, 4, 8, 17, 34, 68, and 136
And, Factors of
162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162
Examples of GCF
Sammy baked 136 chocolate cookies and 162 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 136 and 162.
GCF of 136 and 162 is 2.
A class has 136 boys and 162 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 136 and 162. Hence, GCF of 136 and 162 is 2.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(136, 162) = ( 136 * 162 ) / LCM(136, 162) = 2.
What is the GCF of 136 and 162?GCF of 136 and 162 is 2.
Ram has 136 cans of Pepsi and 162 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 136 and 162. Hence GCF of 136 and 162 is 2. So the number of tables that can be arranged is 2.
Mary has 136 blue buttons and 162 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 136 and 162. Hence, the GCF of 136 and 162 or the greatest arrangement is 2.
Kamal is making identical balloon arrangements for a party. He has 136 maroon balloons, and 162 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 136 and 162. So the GCF of 136 and 162 is 2.
Kunal is making baskets full of nuts and dried fruits. He has 136 bags of nuts and 162 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 136 and 162. So the GCF of 136 and 162 is 2.
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 136 bus tickets and 162 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 136 and 162. Hence, GCF of 136 and 162 is 2.