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. 448 and 1000 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 448 and also of 1000.
- Every number is a factor of zero (0), since 448 x 0 = 0 and 1000 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, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448 are exact divisors of 448 and 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 are exact divisors of 1000.
- Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448. Each factor divides 448 without leaving a remainder.
Simlarly, factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000. Each factor divides 1000 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448 are all less than or equal to 448 and 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 are all less than or equal to 1000.
Steps to find Factors of 448 and 1000
- Step 1. Find all the numbers that would divide 448 and 1000 without leaving any remainder. Starting with the number 1 upto 224 (half of 448) and 1 upto 500 (half of 1000). The number 1 and the number itself are always factors of the given number.
448 ÷ 1 : Remainder = 0
1000 ÷ 1 : Remainder = 0
448 ÷ 2 : Remainder = 0
1000 ÷ 2 : Remainder = 0
448 ÷ 4 : Remainder = 0
1000 ÷ 4 : Remainder = 0
448 ÷ 7 : Remainder = 0
1000 ÷ 5 : Remainder = 0
448 ÷ 8 : Remainder = 0
1000 ÷ 8 : Remainder = 0
448 ÷ 14 : Remainder = 0
1000 ÷ 10 : Remainder = 0
448 ÷ 16 : Remainder = 0
1000 ÷ 20 : Remainder = 0
448 ÷ 28 : Remainder = 0
1000 ÷ 25 : Remainder = 0
448 ÷ 32 : Remainder = 0
1000 ÷ 40 : Remainder = 0
448 ÷ 56 : Remainder = 0
1000 ÷ 50 : Remainder = 0
448 ÷ 64 : Remainder = 0
1000 ÷ 100 : Remainder = 0
448 ÷ 112 : Remainder = 0
1000 ÷ 125 : Remainder = 0
448 ÷ 224 : Remainder = 0
1000 ÷ 200 : Remainder = 0
448 ÷ 448 : Remainder = 0
1000 ÷ 250 : Remainder = 0
1000 ÷ 500 : Remainder = 0
1000 ÷ 1000 : Remainder = 0
Hence, Factors of
448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, and 448
And, Factors of
1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000
Examples of GCF
Sammy baked 448 chocolate cookies and 1000 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 448 and 1000.
GCF of 448 and 1000 is 8.
A class has 448 boys and 1000 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 448 and 1000. Hence, GCF of 448 and 1000 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(448, 1000) = ( 448 * 1000 ) / LCM(448, 1000) = 8.
What is the GCF of 448 and 1000?GCF of 448 and 1000 is 8.
Ariel is making ready to eat meals to share with friends. She has 448 bottles of water and 1000 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 448 and 1000. So the GCF of 448 and 1000 is 8.
Mary has 448 blue buttons and 1000 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 448 and 1000. Hence, the GCF of 448 and 1000 or the greatest arrangement is 8.
Kamal is making identical balloon arrangements for a party. He has 448 maroon balloons, and 1000 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 448 and 1000. So the GCF of 448 and 1000 is 8.
Kunal is making baskets full of nuts and dried fruits. He has 448 bags of nuts and 1000 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 448 and 1000. So the GCF of 448 and 1000 is 8.