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. 48 and 128 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 48 and also of 128.
- Every number is a factor of zero (0), since 48 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, 48 are exact divisors of 48 and 1, 2, 4, 8, 16, 32, 64, 128 are exact divisors of 128.
- Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Each factor divides 48 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, 48 are all less than or equal to 48 and 1, 2, 4, 8, 16, 32, 64, 128 are all less than or equal to 128.
Steps to find Factors of 48 and 128
- Step 1. Find all the numbers that would divide 48 and 128 without leaving any remainder. Starting with the number 1 upto 24 (half of 48) and 1 upto 64 (half of 128). The number 1 and the number itself are always factors of the given number.
48 ÷ 1 : Remainder = 0
128 ÷ 1 : Remainder = 0
48 ÷ 2 : Remainder = 0
128 ÷ 2 : Remainder = 0
48 ÷ 3 : Remainder = 0
128 ÷ 4 : Remainder = 0
48 ÷ 4 : Remainder = 0
128 ÷ 8 : Remainder = 0
48 ÷ 6 : Remainder = 0
128 ÷ 16 : Remainder = 0
48 ÷ 8 : Remainder = 0
128 ÷ 32 : Remainder = 0
48 ÷ 12 : Remainder = 0
128 ÷ 64 : Remainder = 0
48 ÷ 16 : Remainder = 0
128 ÷ 128 : Remainder = 0
Hence, Factors of
48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
And, Factors of
128 are 1, 2, 4, 8, 16, 32, 64, and 128
Examples of GCF
Sammy baked 48 chocolate cookies and 128 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 48 and 128.
GCF of 48 and 128 is 16.
A class has 48 boys and 128 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 48 and 128. Hence, GCF of 48 and 128 is 16.
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.
Ram has 48 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 48 and 128. Hence GCF of 48 and 128 is 16. So the number of tables that can be arranged is 16.
Ariel is making ready to eat meals to share with friends. She has 48 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 48 and 128. So the GCF of 48 and 128 is 16.
Mary has 48 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 48 and 128. Hence, the GCF of 48 and 128 or the greatest arrangement is 16.
Kamal is making identical balloon arrangements for a party. He has 48 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 48 and 128. So the GCF of 48 and 128 is 16.
Kunal is making baskets full of nuts and dried fruits. He has 48 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 48 and 128. So the GCF of 48 and 128 is 16.
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 48 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 48 and 128. Hence, GCF of 48 and 128 is 16.