How do you explain factors?
In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 512 and 648 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 512 and also of 648.
- Every number is a factor of zero (0), since 512 x 0 = 0 and 648 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 are exact divisors of 512 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648 are exact divisors of 648.
- Factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. Each factor divides 512 without leaving a remainder.
Simlarly, factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648. Each factor divides 648 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 are all less than or equal to 512 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648 are all less than or equal to 648.
Steps to find Factors of 512 and 648
- Step 1. Find all the numbers that would divide 512 and 648 without leaving any remainder. Starting with the number 1 upto 256 (half of 512) and 1 upto 324 (half of 648). The number 1 and the number itself are always factors of the given number.
512 ÷ 1 : Remainder = 0
648 ÷ 1 : Remainder = 0
512 ÷ 2 : Remainder = 0
648 ÷ 2 : Remainder = 0
512 ÷ 4 : Remainder = 0
648 ÷ 3 : Remainder = 0
512 ÷ 8 : Remainder = 0
648 ÷ 4 : Remainder = 0
512 ÷ 16 : Remainder = 0
648 ÷ 6 : Remainder = 0
512 ÷ 32 : Remainder = 0
648 ÷ 8 : Remainder = 0
512 ÷ 64 : Remainder = 0
648 ÷ 9 : Remainder = 0
512 ÷ 128 : Remainder = 0
648 ÷ 12 : Remainder = 0
512 ÷ 256 : Remainder = 0
648 ÷ 18 : Remainder = 0
512 ÷ 512 : Remainder = 0
648 ÷ 24 : Remainder = 0
648 ÷ 108 : Remainder = 0
648 ÷ 162 : Remainder = 0
648 ÷ 216 : Remainder = 0
648 ÷ 324 : Remainder = 0
648 ÷ 648 : Remainder = 0
Hence, Factors of
512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512
And, Factors of
648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648
Examples of GCF
Sammy baked 512 chocolate cookies and 648 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 512 and 648.
GCF of 512 and 648 is 8.
A class has 512 boys and 648 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 512 and 648. Hence, GCF of 512 and 648 is 8.
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(512, 648) = ( 512 * 648 ) / LCM(512, 648) = 8.
What is the GCF of 512 and 648?GCF of 512 and 648 is 8.
Ariel is making ready to eat meals to share with friends. She has 512 bottles of water and 648 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 512 and 648. So the GCF of 512 and 648 is 8.
Mary has 512 blue buttons and 648 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 512 and 648. Hence, the GCF of 512 and 648 or the greatest arrangement is 8.
Kamal is making identical balloon arrangements for a party. He has 512 maroon balloons, and 648 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 512 and 648. So the GCF of 512 and 648 is 8.
Kunal is making baskets full of nuts and dried fruits. He has 512 bags of nuts and 648 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 512 and 648. So the GCF of 512 and 648 is 8.
A class has 512 boys and 648 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 512 and 648. Hence, GCF of 512 and 648 is 8.