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. 132 and 242 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 132 and also of 242.
- Every number is a factor of zero (0), since 132 x 0 = 0 and 242 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, 11, 12, 22, 33, 44, 66, 132 are exact divisors of 132 and 1, 2, 11, 22, 121, 242 are exact divisors of 242.
- Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. Each factor divides 132 without leaving a remainder.
Simlarly, factors of 242 are 1, 2, 11, 22, 121, 242. Each factor divides 242 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 are all less than or equal to 132 and 1, 2, 11, 22, 121, 242 are all less than or equal to 242.
Steps to find Factors of 132 and 242
- Step 1. Find all the numbers that would divide 132 and 242 without leaving any remainder. Starting with the number 1 upto 66 (half of 132) and 1 upto 121 (half of 242). The number 1 and the number itself are always factors of the given number.
132 ÷ 1 : Remainder = 0
242 ÷ 1 : Remainder = 0
132 ÷ 2 : Remainder = 0
242 ÷ 2 : Remainder = 0
132 ÷ 3 : Remainder = 0
242 ÷ 11 : Remainder = 0
132 ÷ 4 : Remainder = 0
242 ÷ 22 : Remainder = 0
132 ÷ 6 : Remainder = 0
242 ÷ 121 : Remainder = 0
132 ÷ 11 : Remainder = 0
242 ÷ 242 : Remainder = 0
132 ÷ 132 : Remainder = 0
Hence, Factors of
132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132
And, Factors of
242 are 1, 2, 11, 22, 121, and 242
Examples of GCF
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(132, 242) = ( 132 * 242 ) / LCM(132, 242) = 22.
What is the GCF of 132 and 242?GCF of 132 and 242 is 22.
Ram has 132 cans of Pepsi and 242 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 132 and 242. Hence GCF of 132 and 242 is 22. So the number of tables that can be arranged is 22.
Rubel is creating individual servings of starters for her birthday party. He has 132 pizzas and 242 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 132 and 242. Thus GCF of 132 and 242 is 22.
Ariel is making ready to eat meals to share with friends. She has 132 bottles of water and 242 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 132 and 242. So the GCF of 132 and 242 is 22.
Mary has 132 blue buttons and 242 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 132 and 242. Hence, the GCF of 132 and 242 or the greatest arrangement is 22.
Kamal is making identical balloon arrangements for a party. He has 132 maroon balloons, and 242 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 132 and 242. So the GCF of 132 and 242 is 22.
Kunal is making baskets full of nuts and dried fruits. He has 132 bags of nuts and 242 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 132 and 242. So the GCF of 132 and 242 is 22.
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 132 bus tickets and 242 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 132 and 242. Hence, GCF of 132 and 242 is 22.