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. 168 and 196 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 168 and also of 196.
- Every number is a factor of zero (0), since 168 x 0 = 0 and 196 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, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 are exact divisors of 168 and 1, 2, 4, 7, 14, 28, 49, 98, 196 are exact divisors of 196.
- 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.
Simlarly, factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196. Each factor divides 196 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 are all less than or equal to 168 and 1, 2, 4, 7, 14, 28, 49, 98, 196 are all less than or equal to 196.
Steps to find Factors of 168 and 196
- Step 1. Find all the numbers that would divide 168 and 196 without leaving any remainder. Starting with the number 1 upto 84 (half of 168) and 1 upto 98 (half of 196). The number 1 and the number itself are always factors of the given number.
168 ÷ 1 : Remainder = 0
196 ÷ 1 : Remainder = 0
168 ÷ 2 : Remainder = 0
196 ÷ 2 : Remainder = 0
168 ÷ 3 : Remainder = 0
196 ÷ 4 : Remainder = 0
168 ÷ 4 : Remainder = 0
196 ÷ 7 : Remainder = 0
168 ÷ 6 : Remainder = 0
196 ÷ 14 : Remainder = 0
168 ÷ 7 : Remainder = 0
196 ÷ 28 : Remainder = 0
168 ÷ 8 : Remainder = 0
196 ÷ 49 : Remainder = 0
168 ÷ 12 : Remainder = 0
196 ÷ 98 : Remainder = 0
168 ÷ 14 : Remainder = 0
196 ÷ 196 : Remainder = 0
168 ÷ 168 : Remainder = 0
Hence, Factors of
168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168
And, Factors of
196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196
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(168, 196) = ( 168 * 196 ) / LCM(168, 196) = 28.
What is the GCF of 168 and 196?GCF of 168 and 196 is 28.
Ram has 168 cans of Pepsi and 196 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 168 and 196. Hence GCF of 168 and 196 is 28. So the number of tables that can be arranged is 28.
Rubel is creating individual servings of starters for her birthday party. He has 168 pizzas and 196 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 168 and 196. Thus GCF of 168 and 196 is 28.
Ariel is making ready to eat meals to share with friends. She has 168 bottles of water and 196 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 168 and 196. So the GCF of 168 and 196 is 28.
Mary has 168 blue buttons and 196 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 168 and 196. Hence, the GCF of 168 and 196 or the greatest arrangement is 28.
Kamal is making identical balloon arrangements for a party. He has 168 maroon balloons, and 196 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 168 and 196. So the GCF of 168 and 196 is 28.
Kunal is making baskets full of nuts and dried fruits. He has 168 bags of nuts and 196 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 168 and 196. So the GCF of 168 and 196 is 28.
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 168 bus tickets and 196 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 168 and 196. Hence, GCF of 168 and 196 is 28.