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 120 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 48 and also of 120.
- Every number is a factor of zero (0), since 48 x 0 = 0 and 120 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, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 are exact divisors of 120.
- 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 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Each factor divides 120 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, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 are all less than or equal to 120.
Steps to find Factors of 48 and 120
- Step 1. Find all the numbers that would divide 48 and 120 without leaving any remainder. Starting with the number 1 upto 24 (half of 48) and 1 upto 60 (half of 120). The number 1 and the number itself are always factors of the given number.
48 ÷ 1 : Remainder = 0
120 ÷ 1 : Remainder = 0
48 ÷ 2 : Remainder = 0
120 ÷ 2 : Remainder = 0
48 ÷ 3 : Remainder = 0
120 ÷ 3 : Remainder = 0
48 ÷ 4 : Remainder = 0
120 ÷ 4 : Remainder = 0
48 ÷ 6 : Remainder = 0
120 ÷ 5 : Remainder = 0
48 ÷ 8 : Remainder = 0
120 ÷ 6 : Remainder = 0
48 ÷ 12 : Remainder = 0
120 ÷ 8 : Remainder = 0
48 ÷ 16 : Remainder = 0
120 ÷ 10 : Remainder = 0
48 ÷ 24 : Remainder = 0
120 ÷ 12 : Remainder = 0
48 ÷ 48 : Remainder = 0
120 ÷ 15 : Remainder = 0
120 ÷ 120 : Remainder = 0
Hence, Factors of
48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
And, Factors of
120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120
Examples of GCF
Sammy baked 48 chocolate cookies and 120 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 120.
GCF of 48 and 120 is 24.
A class has 48 boys and 120 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 120. Hence, GCF of 48 and 120 is 24.
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 120 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 120. Hence GCF of 48 and 120 is 24. So the number of tables that can be arranged is 24.
Ariel is making ready to eat meals to share with friends. She has 48 bottles of water and 120 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 120. So the GCF of 48 and 120 is 24.
Mary has 48 blue buttons and 120 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 120. Hence, the GCF of 48 and 120 or the greatest arrangement is 24.
Kamal is making identical balloon arrangements for a party. He has 48 maroon balloons, and 120 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 120. So the GCF of 48 and 120 is 24.
Kunal is making baskets full of nuts and dried fruits. He has 48 bags of nuts and 120 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 120. So the GCF of 48 and 120 is 24.
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 120 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 120. Hence, GCF of 48 and 120 is 24.