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. 400 and 1080 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 400 and also of 1080.
- Every number is a factor of zero (0), since 400 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, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 are exact divisors of 400 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 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. Each factor divides 400 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, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 are all less than or equal to 400 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 400 and 1080
- Step 1. Find all the numbers that would divide 400 and 1080 without leaving any remainder. Starting with the number 1 upto 200 (half of 400) and 1 upto 540 (half of 1080). The number 1 and the number itself are always factors of the given number.
400 ÷ 1 : Remainder = 0
1080 ÷ 1 : Remainder = 0
400 ÷ 2 : Remainder = 0
1080 ÷ 2 : Remainder = 0
400 ÷ 4 : Remainder = 0
1080 ÷ 3 : Remainder = 0
400 ÷ 5 : Remainder = 0
1080 ÷ 4 : Remainder = 0
400 ÷ 8 : Remainder = 0
1080 ÷ 5 : Remainder = 0
400 ÷ 10 : Remainder = 0
1080 ÷ 6 : Remainder = 0
400 ÷ 16 : Remainder = 0
1080 ÷ 8 : Remainder = 0
400 ÷ 20 : Remainder = 0
1080 ÷ 9 : Remainder = 0
400 ÷ 25 : Remainder = 0
1080 ÷ 10 : Remainder = 0
400 ÷ 40 : Remainder = 0
1080 ÷ 12 : Remainder = 0
400 ÷ 50 : Remainder = 0
1080 ÷ 15 : Remainder = 0
400 ÷ 80 : Remainder = 0
1080 ÷ 18 : Remainder = 0
400 ÷ 100 : Remainder = 0
1080 ÷ 20 : Remainder = 0
400 ÷ 200 : Remainder = 0
1080 ÷ 24 : Remainder = 0
400 ÷ 400 : Remainder = 0
1080 ÷ 27 : Remainder = 0
1080 ÷ 30 : Remainder = 0
1080 ÷ 36 : Remainder = 0
1080 ÷ 40 : Remainder = 0
1080 ÷ 45 : Remainder = 0
1080 ÷ 54 : Remainder = 0
1080 ÷ 60 : Remainder = 0
1080 ÷ 72 : Remainder = 0
1080 ÷ 90 : Remainder = 0
1080 ÷ 108 : Remainder = 0
1080 ÷ 120 : Remainder = 0
1080 ÷ 135 : Remainder = 0
1080 ÷ 180 : Remainder = 0
1080 ÷ 216 : Remainder = 0
1080 ÷ 270 : Remainder = 0
1080 ÷ 360 : Remainder = 0
1080 ÷ 540 : Remainder = 0
1080 ÷ 1080 : Remainder = 0
Hence, Factors of
400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400
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 400 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 400 and 1080.
GCF of 400 and 1080 is 40.
A class has 400 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 400 and 1080. Hence, GCF of 400 and 1080 is 40.
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(400, 1080) = ( 400 * 1080 ) / LCM(400, 1080) = 40.
What is the GCF of 400 and 1080?GCF of 400 and 1080 is 40.
Mary has 400 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 400 and 1080. Hence, the GCF of 400 and 1080 or the greatest arrangement is 40.
Kamal is making identical balloon arrangements for a party. He has 400 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 400 and 1080. So the GCF of 400 and 1080 is 40.
Kunal is making baskets full of nuts and dried fruits. He has 400 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 400 and 1080. So the GCF of 400 and 1080 is 40.
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 400 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 400 and 1080. Hence, GCF of 400 and 1080 is 40.