How can we define factors?
In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.
Properties of Factors
- Each number is a factor of itself. Eg. 1024 and 2016 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 1024 and also of 2016.
- Every number is a factor of zero (0), since 1024 x 0 = 0 and 2016 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, 512, 1024 are exact divisors of 1024 and 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016 are exact divisors of 2016.
- Factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Each factor divides 1024 without leaving a remainder.
Simlarly, factors of 2016 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016. Each factor divides 2016 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, 512, 1024 are all less than or equal to 1024 and 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016 are all less than or equal to 2016.
Steps to find Factors of 1024 and 2016
- Step 1. Find all the numbers that would divide 1024 and 2016 without leaving any remainder. Starting with the number 1 upto 512 (half of 1024) and 1 upto 1008 (half of 2016). The number 1 and the number itself are always factors of the given number.
1024 ÷ 1 : Remainder = 0
2016 ÷ 1 : Remainder = 0
1024 ÷ 2 : Remainder = 0
2016 ÷ 2 : Remainder = 0
1024 ÷ 4 : Remainder = 0
2016 ÷ 3 : Remainder = 0
1024 ÷ 8 : Remainder = 0
2016 ÷ 4 : Remainder = 0
1024 ÷ 16 : Remainder = 0
2016 ÷ 6 : Remainder = 0
1024 ÷ 32 : Remainder = 0
2016 ÷ 7 : Remainder = 0
1024 ÷ 64 : Remainder = 0
2016 ÷ 8 : Remainder = 0
1024 ÷ 128 : Remainder = 0
2016 ÷ 9 : Remainder = 0
1024 ÷ 256 : Remainder = 0
2016 ÷ 12 : Remainder = 0
1024 ÷ 512 : Remainder = 0
2016 ÷ 14 : Remainder = 0
1024 ÷ 1024 : Remainder = 0
2016 ÷ 16 : Remainder = 0
2016 ÷ 18 : Remainder = 0
2016 ÷ 21 : Remainder = 0
2016 ÷ 24 : Remainder = 0
2016 ÷ 28 : Remainder = 0
2016 ÷ 32 : Remainder = 0
2016 ÷ 36 : Remainder = 0
2016 ÷ 42 : Remainder = 0
2016 ÷ 48 : Remainder = 0
2016 ÷ 56 : Remainder = 0
2016 ÷ 63 : Remainder = 0
2016 ÷ 72 : Remainder = 0
2016 ÷ 84 : Remainder = 0
2016 ÷ 96 : Remainder = 0
2016 ÷ 112 : Remainder = 0
2016 ÷ 126 : Remainder = 0
2016 ÷ 144 : Remainder = 0
2016 ÷ 168 : Remainder = 0
2016 ÷ 224 : Remainder = 0
2016 ÷ 252 : Remainder = 0
2016 ÷ 288 : Remainder = 0
2016 ÷ 336 : Remainder = 0
2016 ÷ 504 : Remainder = 0
2016 ÷ 672 : Remainder = 0
2016 ÷ 1008 : Remainder = 0
2016 ÷ 2016 : Remainder = 0
Hence, Factors of
1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024
And, Factors of
2016 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, and 2016
Examples of GCF
Sammy baked 1024 chocolate cookies and 2016 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 1024 and 2016.
GCF of 1024 and 2016 is 32.
A class has 1024 boys and 2016 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 1024 and 2016. Hence, GCF of 1024 and 2016 is 32.
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(1024, 2016) = ( 1024 * 2016 ) / LCM(1024, 2016) = 32.
What is the GCF of 1024 and 2016?GCF of 1024 and 2016 is 32.
Ariel is making ready to eat meals to share with friends. She has 1024 bottles of water and 2016 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 1024 and 2016. So the GCF of 1024 and 2016 is 32.
Mary has 1024 blue buttons and 2016 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 1024 and 2016. Hence, the GCF of 1024 and 2016 or the greatest arrangement is 32.
Kamal is making identical balloon arrangements for a party. He has 1024 maroon balloons, and 2016 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 1024 and 2016. So the GCF of 1024 and 2016 is 32.
Kunal is making baskets full of nuts and dried fruits. He has 1024 bags of nuts and 2016 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 1024 and 2016. So the GCF of 1024 and 2016 is 32.