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 36 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 8 and also of 36.
- Every number is a factor of zero (0), since 8 x 0 = 0 and 36 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, 3, 4, 6, 9, 12, 18, 36 are exact divisors of 36.
- Factors of 8 are 1, 2, 4, 8. Each factor divides 8 without leaving a remainder.
Simlarly, factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Each factor divides 36 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, 3, 4, 6, 9, 12, 18, 36 are all less than or equal to 36.
Steps to find Factors of 8 and 36
- Step 1. Find all the numbers that would divide 8 and 36 without leaving any remainder. Starting with the number 1 upto 4 (half of 8) and 1 upto 18 (half of 36). The number 1 and the number itself are always factors of the given number.
8 ÷ 1 : Remainder = 0
36 ÷ 1 : Remainder = 0
8 ÷ 2 : Remainder = 0
36 ÷ 2 : Remainder = 0
8 ÷ 4 : Remainder = 0
36 ÷ 3 : Remainder = 0
8 ÷ 8 : Remainder = 0
36 ÷ 4 : Remainder = 0
Hence, Factors of
8 are 1, 2, 4, and 8
And, Factors of
36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36
Examples of GCF
Sammy baked 8 chocolate cookies and 36 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 36.
GCF of 8 and 36 is 4.
A class has 8 boys and 36 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 36. Hence, GCF of 8 and 36 is 4.
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, 36) = ( 8 * 36 ) / LCM(8, 36) = 4.
What is the GCF of 8 and 36?GCF of 8 and 36 is 4.
Ariel is making ready to eat meals to share with friends. She has 8 bottles of water and 36 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 36. So the GCF of 8 and 36 is 4.
Mary has 8 blue buttons and 36 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 36. Hence, the GCF of 8 and 36 or the greatest arrangement is 4.
Kamal is making identical balloon arrangements for a party. He has 8 maroon balloons, and 36 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 36. So the GCF of 8 and 36 is 4.
Kunal is making baskets full of nuts and dried fruits. He has 8 bags of nuts and 36 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 36. So the GCF of 8 and 36 is 4.
A class has 8 boys and 36 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 36. Hence, GCF of 8 and 36 is 4.