What is the definition of factors?
In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.
Properties of Factors
- Each number is a factor of itself. Eg. 8 and 40 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 8 and also of 40.
- Every number is a factor of zero (0), since 8 x 0 = 0 and 40 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 are exact divisors of 8 and 1, 2, 4, 5, 8, 10, 20, 40 are exact divisors of 40.
- Factors of 8 are 1, 2, 4, 8. Each factor divides 8 without leaving a remainder.
Simlarly, factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. Each factor divides 40 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8 are all less than or equal to 8 and 1, 2, 4, 5, 8, 10, 20, 40 are all less than or equal to 40.
Steps to find Factors of 8 and 40
- Step 1. Find all the numbers that would divide 8 and 40 without leaving any remainder. Starting with the number 1 upto 4 (half of 8) and 1 upto 20 (half of 40). The number 1 and the number itself are always factors of the given number.
8 ÷ 1 : Remainder = 0
40 ÷ 1 : Remainder = 0
8 ÷ 2 : Remainder = 0
40 ÷ 2 : Remainder = 0
8 ÷ 4 : Remainder = 0
40 ÷ 4 : Remainder = 0
8 ÷ 8 : Remainder = 0
40 ÷ 5 : Remainder = 0
Hence, Factors of
8 are 1, 2, 4, and 8
And, Factors of
40 are 1, 2, 4, 5, 8, 10, 20, and 40
Examples of GCF
Sammy baked 8 chocolate cookies and 40 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 8 and 40.
GCF of 8 and 40 is 8.
A class has 8 boys and 40 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 8 and 40. Hence, GCF of 8 and 40 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(8, 40) = ( 8 * 40 ) / LCM(8, 40) = 8.
What is the GCF of 8 and 40?GCF of 8 and 40 is 8.
Ariel is making ready to eat meals to share with friends. She has 8 bottles of water and 40 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 8 and 40. So the GCF of 8 and 40 is 8.
Mary has 8 blue buttons and 40 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 8 and 40. Hence, the GCF of 8 and 40 or the greatest arrangement is 8.
Kamal is making identical balloon arrangements for a party. He has 8 maroon balloons, and 40 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 8 and 40. So the GCF of 8 and 40 is 8.
Kunal is making baskets full of nuts and dried fruits. He has 8 bags of nuts and 40 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 8 and 40. So the GCF of 8 and 40 is 8.
A class has 8 boys and 40 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 8 and 40. Hence, GCF of 8 and 40 is 8.