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. 96 and 128 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 96 and also of 128.
- Every number is a factor of zero (0), since 96 x 0 = 0 and 128 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, 8, 12, 16, 24, 32, 48, 96 are exact divisors of 96 and 1, 2, 4, 8, 16, 32, 64, 128 are exact divisors of 128.
- Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. Each factor divides 96 without leaving a remainder.
Simlarly, factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128. Each factor divides 128 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 are all less than or equal to 96 and 1, 2, 4, 8, 16, 32, 64, 128 are all less than or equal to 128.
Steps to find Factors of 96 and 128
- Step 1. Find all the numbers that would divide 96 and 128 without leaving any remainder. Starting with the number 1 upto 48 (half of 96) and 1 upto 64 (half of 128). The number 1 and the number itself are always factors of the given number.
96 ÷ 1 : Remainder = 0
128 ÷ 1 : Remainder = 0
96 ÷ 2 : Remainder = 0
128 ÷ 2 : Remainder = 0
96 ÷ 3 : Remainder = 0
128 ÷ 4 : Remainder = 0
96 ÷ 4 : Remainder = 0
128 ÷ 8 : Remainder = 0
96 ÷ 6 : Remainder = 0
128 ÷ 16 : Remainder = 0
96 ÷ 8 : Remainder = 0
128 ÷ 32 : Remainder = 0
96 ÷ 12 : Remainder = 0
128 ÷ 64 : Remainder = 0
96 ÷ 16 : Remainder = 0
128 ÷ 128 : Remainder = 0
Hence, Factors of
96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
And, Factors of
128 are 1, 2, 4, 8, 16, 32, 64, and 128
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(96, 128) = ( 96 * 128 ) / LCM(96, 128) = 32.
What is the GCF of 96 and 128?GCF of 96 and 128 is 32.
Ram has 96 cans of Pepsi and 128 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 96 and 128. Hence GCF of 96 and 128 is 32. So the number of tables that can be arranged is 32.
Rubel is creating individual servings of starters for her birthday party. He has 96 pizzas and 128 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 96 and 128. Thus GCF of 96 and 128 is 32.
Ariel is making ready to eat meals to share with friends. She has 96 bottles of water and 128 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 96 and 128. So the GCF of 96 and 128 is 32.
Mary has 96 blue buttons and 128 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 96 and 128. Hence, the GCF of 96 and 128 or the greatest arrangement is 32.
Kamal is making identical balloon arrangements for a party. He has 96 maroon balloons, and 128 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 96 and 128. So the GCF of 96 and 128 is 32.
Kunal is making baskets full of nuts and dried fruits. He has 96 bags of nuts and 128 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 96 and 128. So the GCF of 96 and 128 is 32.
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 96 bus tickets and 128 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 96 and 128. Hence, GCF of 96 and 128 is 32.