What are factors?
In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 1920 and 1080 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 1920 and also of 1080.
- Every number is a factor of zero (0), since 1920 x 0 = 0 and 1080 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, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1920 are exact divisors of 1920 and 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080 are exact divisors of 1080.
- Factors of 1920 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1920. Each factor divides 1920 without leaving a remainder.
Simlarly, factors of 1080 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080. Each factor divides 1080 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1920 are all less than or equal to 1920 and 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080 are all less than or equal to 1080.
Steps to find Factors of 1920 and 1080
- Step 1. Find all the numbers that would divide 1920 and 1080 without leaving any remainder. Starting with the number 1 upto 960 (half of 1920) and 1 upto 540 (half of 1080). The number 1 and the number itself are always factors of the given number.
1920 ÷ 1 : Remainder = 0
1080 ÷ 1 : Remainder = 0
1920 ÷ 2 : Remainder = 0
1080 ÷ 2 : Remainder = 0
1920 ÷ 3 : Remainder = 0
1080 ÷ 3 : Remainder = 0
1920 ÷ 4 : Remainder = 0
1080 ÷ 4 : Remainder = 0
1920 ÷ 5 : Remainder = 0
1080 ÷ 5 : Remainder = 0
1920 ÷ 6 : Remainder = 0
1080 ÷ 6 : Remainder = 0
1920 ÷ 8 : Remainder = 0
1080 ÷ 8 : Remainder = 0
1920 ÷ 10 : Remainder = 0
1080 ÷ 9 : Remainder = 0
1920 ÷ 12 : Remainder = 0
1080 ÷ 10 : Remainder = 0
1920 ÷ 15 : Remainder = 0
1080 ÷ 12 : Remainder = 0
1920 ÷ 16 : Remainder = 0
1080 ÷ 15 : Remainder = 0
1920 ÷ 20 : Remainder = 0
1080 ÷ 18 : Remainder = 0
1920 ÷ 24 : Remainder = 0
1080 ÷ 20 : Remainder = 0
1920 ÷ 30 : Remainder = 0
1080 ÷ 24 : Remainder = 0
1920 ÷ 32 : Remainder = 0
1080 ÷ 27 : Remainder = 0
1920 ÷ 40 : Remainder = 0
1080 ÷ 30 : Remainder = 0
1920 ÷ 48 : Remainder = 0
1080 ÷ 36 : Remainder = 0
1920 ÷ 60 : Remainder = 0
1080 ÷ 40 : Remainder = 0
1920 ÷ 64 : Remainder = 0
1080 ÷ 45 : Remainder = 0
1920 ÷ 80 : Remainder = 0
1080 ÷ 54 : Remainder = 0
1920 ÷ 96 : Remainder = 0
1080 ÷ 60 : Remainder = 0
1920 ÷ 120 : Remainder = 0
1080 ÷ 72 : Remainder = 0
1920 ÷ 128 : Remainder = 0
1080 ÷ 90 : Remainder = 0
1920 ÷ 160 : Remainder = 0
1080 ÷ 108 : Remainder = 0
1920 ÷ 192 : Remainder = 0
1080 ÷ 120 : Remainder = 0
1920 ÷ 240 : Remainder = 0
1080 ÷ 135 : Remainder = 0
1920 ÷ 320 : Remainder = 0
1080 ÷ 180 : Remainder = 0
1920 ÷ 384 : Remainder = 0
1080 ÷ 216 : Remainder = 0
1920 ÷ 480 : Remainder = 0
1080 ÷ 270 : Remainder = 0
1920 ÷ 640 : Remainder = 0
1080 ÷ 360 : Remainder = 0
1920 ÷ 960 : Remainder = 0
1080 ÷ 540 : Remainder = 0
1920 ÷ 1920 : Remainder = 0
1080 ÷ 1080 : Remainder = 0
Hence, Factors of
1920 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, and 1920
And, Factors of
1080 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, and 1080
Examples of GCF
Sammy baked 1920 chocolate cookies and 1080 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 1920 and 1080.
GCF of 1920 and 1080 is 120.
A class has 1920 boys and 1080 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 1920 and 1080. Hence, GCF of 1920 and 1080 is 120.
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 1920 cans of Pepsi and 1080 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 1920 and 1080. Hence GCF of 1920 and 1080 is 120. So the number of tables that can be arranged is 120.
Ariel is making ready to eat meals to share with friends. She has 1920 bottles of water and 1080 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 1920 and 1080. So the GCF of 1920 and 1080 is 120.
Mary has 1920 blue buttons and 1080 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 1920 and 1080. Hence, the GCF of 1920 and 1080 or the greatest arrangement is 120.
Kamal is making identical balloon arrangements for a party. He has 1920 maroon balloons, and 1080 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 1920 and 1080. So the GCF of 1920 and 1080 is 120.
Kunal is making baskets full of nuts and dried fruits. He has 1920 bags of nuts and 1080 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 1920 and 1080. So the GCF of 1920 and 1080 is 120.
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 1920 bus tickets and 1080 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 1920 and 1080. Hence, GCF of 1920 and 1080 is 120.