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. 128 and 192 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 128 and also of 192.
- Every number is a factor of zero (0), since 128 x 0 = 0 and 192 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, 16, 32, 64, 128 are exact divisors of 128 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192 are exact divisors of 192.
- Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128. Each factor divides 128 without leaving a remainder.
Simlarly, factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. Each factor divides 192 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32, 64, 128 are all less than or equal to 128 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192 are all less than or equal to 192.
Steps to find Factors of 128 and 192
- Step 1. Find all the numbers that would divide 128 and 192 without leaving any remainder. Starting with the number 1 upto 64 (half of 128) and 1 upto 96 (half of 192). The number 1 and the number itself are always factors of the given number.
128 ÷ 1 : Remainder = 0
192 ÷ 1 : Remainder = 0
128 ÷ 2 : Remainder = 0
192 ÷ 2 : Remainder = 0
128 ÷ 4 : Remainder = 0
192 ÷ 3 : Remainder = 0
128 ÷ 8 : Remainder = 0
192 ÷ 4 : Remainder = 0
128 ÷ 16 : Remainder = 0
192 ÷ 6 : Remainder = 0
128 ÷ 32 : Remainder = 0
192 ÷ 8 : Remainder = 0
128 ÷ 64 : Remainder = 0
192 ÷ 12 : Remainder = 0
128 ÷ 128 : Remainder = 0
192 ÷ 16 : Remainder = 0
192 ÷ 192 : Remainder = 0
Hence, Factors of
128 are 1, 2, 4, 8, 16, 32, 64, and 128
And, Factors of
192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192
Examples of GCF
A class has 128 boys and 192 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 128 and 192. Hence, GCF of 128 and 192 is 64.
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.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(128, 192) = ( 128 * 192 ) / LCM(128, 192) = 64.
What is the GCF of 128 and 192?GCF of 128 and 192 is 64.
Ram has 128 cans of Pepsi and 192 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 128 and 192. Hence GCF of 128 and 192 is 64. So the number of tables that can be arranged is 64.
Rubel is creating individual servings of starters for her birthday party. He has 128 pizzas and 192 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 128 and 192. Thus GCF of 128 and 192 is 64.
Ariel is making ready to eat meals to share with friends. She has 128 bottles of water and 192 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 128 and 192. So the GCF of 128 and 192 is 64.
Mary has 128 blue buttons and 192 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 128 and 192. Hence, the GCF of 128 and 192 or the greatest arrangement is 64.
Kunal is making baskets full of nuts and dried fruits. He has 128 bags of nuts and 192 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 128 and 192. So the GCF of 128 and 192 is 64.