How can we define factors?
In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 256 and 400 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 256 and also of 400.
- Every number is a factor of zero (0), since 256 x 0 = 0 and 400 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, 256 are exact divisors of 256 and 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 are exact divisors of 400.
- Factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256. Each factor divides 256 without leaving a remainder.
Simlarly, 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. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32, 64, 128, 256 are all less than or equal to 256 and 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 are all less than or equal to 400.
Steps to find Factors of 256 and 400
- Step 1. Find all the numbers that would divide 256 and 400 without leaving any remainder. Starting with the number 1 upto 128 (half of 256) and 1 upto 200 (half of 400). The number 1 and the number itself are always factors of the given number.
256 ÷ 1 : Remainder = 0
400 ÷ 1 : Remainder = 0
256 ÷ 2 : Remainder = 0
400 ÷ 2 : Remainder = 0
256 ÷ 4 : Remainder = 0
400 ÷ 4 : Remainder = 0
256 ÷ 8 : Remainder = 0
400 ÷ 5 : Remainder = 0
256 ÷ 16 : Remainder = 0
400 ÷ 8 : Remainder = 0
256 ÷ 32 : Remainder = 0
400 ÷ 10 : Remainder = 0
256 ÷ 64 : Remainder = 0
400 ÷ 16 : Remainder = 0
256 ÷ 128 : Remainder = 0
400 ÷ 20 : Remainder = 0
256 ÷ 256 : Remainder = 0
400 ÷ 25 : Remainder = 0
400 ÷ 100 : Remainder = 0
400 ÷ 200 : Remainder = 0
400 ÷ 400 : Remainder = 0
Hence, Factors of
256 are 1, 2, 4, 8, 16, 32, 64, 128, and 256
And, Factors of
400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400
Examples of GCF
Sammy baked 256 chocolate cookies and 400 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 256 and 400.
GCF of 256 and 400 is 16.
A class has 256 boys and 400 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 256 and 400. Hence, GCF of 256 and 400 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.
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(256, 400) = ( 256 * 400 ) / LCM(256, 400) = 16.
What is the GCF of 256 and 400?GCF of 256 and 400 is 16.
Mary has 256 blue buttons and 400 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 256 and 400. Hence, the GCF of 256 and 400 or the greatest arrangement is 16.
Kamal is making identical balloon arrangements for a party. He has 256 maroon balloons, and 400 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 256 and 400. So the GCF of 256 and 400 is 16.
Kunal is making baskets full of nuts and dried fruits. He has 256 bags of nuts and 400 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 256 and 400. So the GCF of 256 and 400 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 256 bus tickets and 400 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 256 and 400. Hence, GCF of 256 and 400 is 16.