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. 376 and 600 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 376 and also of 600.
- Every number is a factor of zero (0), since 376 x 0 = 0 and 600 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, 47, 94, 188, 376 are exact divisors of 376 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 are exact divisors of 600.
- Factors of 376 are 1, 2, 4, 8, 47, 94, 188, 376. Each factor divides 376 without leaving a remainder.
Simlarly, factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600. Each factor divides 600 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 47, 94, 188, 376 are all less than or equal to 376 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 are all less than or equal to 600.
Steps to find Factors of 376 and 600
- Step 1. Find all the numbers that would divide 376 and 600 without leaving any remainder. Starting with the number 1 upto 188 (half of 376) and 1 upto 300 (half of 600). The number 1 and the number itself are always factors of the given number.
376 ÷ 1 : Remainder = 0
600 ÷ 1 : Remainder = 0
376 ÷ 2 : Remainder = 0
600 ÷ 2 : Remainder = 0
376 ÷ 4 : Remainder = 0
600 ÷ 3 : Remainder = 0
376 ÷ 8 : Remainder = 0
600 ÷ 4 : Remainder = 0
376 ÷ 47 : Remainder = 0
600 ÷ 5 : Remainder = 0
376 ÷ 94 : Remainder = 0
600 ÷ 6 : Remainder = 0
376 ÷ 188 : Remainder = 0
600 ÷ 8 : Remainder = 0
376 ÷ 376 : Remainder = 0
600 ÷ 10 : Remainder = 0
600 ÷ 100 : Remainder = 0
600 ÷ 120 : Remainder = 0
600 ÷ 150 : Remainder = 0
600 ÷ 200 : Remainder = 0
600 ÷ 300 : Remainder = 0
600 ÷ 600 : Remainder = 0
Hence, Factors of
376 are 1, 2, 4, 8, 47, 94, 188, and 376
And, Factors of
600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600
Examples of GCF
Sammy baked 376 chocolate cookies and 600 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 376 and 600.
GCF of 376 and 600 is 8.
A class has 376 boys and 600 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 376 and 600. Hence, GCF of 376 and 600 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(376, 600) = ( 376 * 600 ) / LCM(376, 600) = 8.
What is the GCF of 376 and 600?GCF of 376 and 600 is 8.
Ariel is making ready to eat meals to share with friends. She has 376 bottles of water and 600 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 376 and 600. So the GCF of 376 and 600 is 8.
Mary has 376 blue buttons and 600 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 376 and 600. Hence, the GCF of 376 and 600 or the greatest arrangement is 8.
Kamal is making identical balloon arrangements for a party. He has 376 maroon balloons, and 600 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 376 and 600. So the GCF of 376 and 600 is 8.
Kunal is making baskets full of nuts and dried fruits. He has 376 bags of nuts and 600 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 376 and 600. So the GCF of 376 and 600 is 8.