What are factors?
In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.
Properties of Factors
- Every factor of a number is an exact divisor of that number, example 1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, 1925 are exact divisors of 1925 and 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 225, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150, 6300 are exact divisors of 6300.
- Every number other than 1 has at least two factors, namely the number itself and 1.
- Each number is a factor of itself. Eg. 1925 and 6300 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 1925 and also of 6300.
Steps to find Factors of 1925 and 6300
- Step 1. Find all the numbers that would divide 1925 and 6300 without leaving any remainder. Starting with the number 1 upto 962 (half of 1925) and 1 upto 3150 (half of 6300). The number 1 and the number itself are always factors of the given number.
1925 ÷ 1 : Remainder = 0
6300 ÷ 1 : Remainder = 0
1925 ÷ 5 : Remainder = 0
6300 ÷ 2 : Remainder = 0
1925 ÷ 7 : Remainder = 0
6300 ÷ 3 : Remainder = 0
1925 ÷ 11 : Remainder = 0
6300 ÷ 4 : Remainder = 0
1925 ÷ 25 : Remainder = 0
6300 ÷ 5 : Remainder = 0
1925 ÷ 35 : Remainder = 0
6300 ÷ 6 : Remainder = 0
1925 ÷ 55 : Remainder = 0
6300 ÷ 7 : Remainder = 0
1925 ÷ 77 : Remainder = 0
6300 ÷ 9 : Remainder = 0
1925 ÷ 175 : Remainder = 0
6300 ÷ 10 : Remainder = 0
1925 ÷ 275 : Remainder = 0
6300 ÷ 12 : Remainder = 0
1925 ÷ 385 : Remainder = 0
6300 ÷ 14 : Remainder = 0
1925 ÷ 1925 : Remainder = 0
6300 ÷ 15 : Remainder = 0
6300 ÷ 18 : Remainder = 0
6300 ÷ 20 : Remainder = 0
6300 ÷ 21 : Remainder = 0
6300 ÷ 25 : Remainder = 0
6300 ÷ 28 : Remainder = 0
6300 ÷ 30 : Remainder = 0
6300 ÷ 35 : Remainder = 0
6300 ÷ 36 : Remainder = 0
6300 ÷ 42 : Remainder = 0
6300 ÷ 45 : Remainder = 0
6300 ÷ 50 : Remainder = 0
6300 ÷ 60 : Remainder = 0
6300 ÷ 63 : Remainder = 0
6300 ÷ 70 : Remainder = 0
6300 ÷ 75 : Remainder = 0
6300 ÷ 84 : Remainder = 0
6300 ÷ 90 : Remainder = 0
6300 ÷ 100 : Remainder = 0
6300 ÷ 105 : Remainder = 0
6300 ÷ 126 : Remainder = 0
6300 ÷ 140 : Remainder = 0
6300 ÷ 150 : Remainder = 0
6300 ÷ 175 : Remainder = 0
6300 ÷ 180 : Remainder = 0
6300 ÷ 210 : Remainder = 0
6300 ÷ 225 : Remainder = 0
6300 ÷ 252 : Remainder = 0
6300 ÷ 300 : Remainder = 0
6300 ÷ 315 : Remainder = 0
6300 ÷ 350 : Remainder = 0
6300 ÷ 420 : Remainder = 0
6300 ÷ 450 : Remainder = 0
6300 ÷ 525 : Remainder = 0
6300 ÷ 630 : Remainder = 0
6300 ÷ 700 : Remainder = 0
6300 ÷ 900 : Remainder = 0
6300 ÷ 1050 : Remainder = 0
6300 ÷ 1260 : Remainder = 0
6300 ÷ 1575 : Remainder = 0
6300 ÷ 2100 : Remainder = 0
6300 ÷ 3150 : Remainder = 0
6300 ÷ 6300 : Remainder = 0
Hence, Factors of
1925 are 1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, and 1925
And, Factors of
6300 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 225, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150, and 6300
Examples of GCF
Sammy baked 1925 chocolate cookies and 6300 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 1925 and 6300.
GCF of 1925 and 6300 is 175.
A class has 1925 boys and 6300 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 1925 and 6300. Hence, GCF of 1925 and 6300 is 175.
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(1925, 6300) = ( 1925 * 6300 ) / LCM(1925, 6300) = 175.
What is the GCF of 1925 and 6300?GCF of 1925 and 6300 is 175.
Ariel is making ready to eat meals to share with friends. She has 1925 bottles of water and 6300 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 1925 and 6300. So the GCF of 1925 and 6300 is 175.
Mary has 1925 blue buttons and 6300 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 1925 and 6300. Hence, the GCF of 1925 and 6300 or the greatest arrangement is 175.
Kamal is making identical balloon arrangements for a party. He has 1925 maroon balloons, and 6300 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 1925 and 6300. So the GCF of 1925 and 6300 is 175.
Kunal is making baskets full of nuts and dried fruits. He has 1925 bags of nuts and 6300 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 1925 and 6300. So the GCF of 1925 and 6300 is 175.
A class has 1925 boys and 6300 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 1925 and 6300. Hence, GCF of 1925 and 6300 is 175.