How do you explain GCF in mathematics?
GCF or greatest common factor of two or more numbers is defined as largest possible number or integer which is the factor of all given number or in other words we can say that largest possible common number which completely divides the given numbers. GCF of two numbers can be represented as GCF (4624, 3825).
Properties of GCF
- The GCF of two or more given numbers cannot be greater than any of the given number. Eg- GCF of 4624 and 3825 is 17, where 17 is less than both 4624 and 3825.
- GCF of two consecutive numbers is always 1.
- The product of GCF and LCM of two given numbers is equal to the product of two numbers.
- The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
How can we define factors?
In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.
Properties of Factors
- Each number is a factor of itself. Eg. 4624 and 3825 are factors of themselves respectively.
- 1 is a factor of every number. Eg. 1 is a factor of 4624 and also of 3825.
- Every number is a factor of zero (0), since 4624 x 0 = 0 and 3825 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, 16, 17, 34, 68, 136, 272, 289, 578, 1156, 2312, 4624 are exact divisors of 4624 and 1, 3, 5, 9, 15, 17, 25, 45, 51, 75, 85, 153, 225, 255, 425, 765, 1275, 3825 are exact divisors of 3825.
- Factors of 4624 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272, 289, 578, 1156, 2312, 4624. Each factor divides 4624 without leaving a remainder.
Simlarly, factors of 3825 are 1, 3, 5, 9, 15, 17, 25, 45, 51, 75, 85, 153, 225, 255, 425, 765, 1275, 3825. Each factor divides 3825 without leaving a remainder. - Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 17, 34, 68, 136, 272, 289, 578, 1156, 2312, 4624 are all less than or equal to 4624 and 1, 3, 5, 9, 15, 17, 25, 45, 51, 75, 85, 153, 225, 255, 425, 765, 1275, 3825 are all less than or equal to 3825.
Steps to find Factors of 4624 and 3825
- Step 1. Find all the numbers that would divide 4624 and 3825 without leaving any remainder. Starting with the number 1 upto 2312 (half of 4624) and 1 upto 1912 (half of 3825). The number 1 and the number itself are always factors of the given number.
4624 ÷ 1 : Remainder = 0
3825 ÷ 1 : Remainder = 0
4624 ÷ 2 : Remainder = 0
3825 ÷ 3 : Remainder = 0
4624 ÷ 4 : Remainder = 0
3825 ÷ 5 : Remainder = 0
4624 ÷ 8 : Remainder = 0
3825 ÷ 9 : Remainder = 0
4624 ÷ 16 : Remainder = 0
3825 ÷ 15 : Remainder = 0
4624 ÷ 17 : Remainder = 0
3825 ÷ 17 : Remainder = 0
4624 ÷ 34 : Remainder = 0
3825 ÷ 25 : Remainder = 0
4624 ÷ 68 : Remainder = 0
3825 ÷ 45 : Remainder = 0
4624 ÷ 136 : Remainder = 0
3825 ÷ 51 : Remainder = 0
4624 ÷ 272 : Remainder = 0
3825 ÷ 75 : Remainder = 0
4624 ÷ 289 : Remainder = 0
3825 ÷ 85 : Remainder = 0
4624 ÷ 578 : Remainder = 0
3825 ÷ 153 : Remainder = 0
4624 ÷ 1156 : Remainder = 0
3825 ÷ 225 : Remainder = 0
4624 ÷ 2312 : Remainder = 0
3825 ÷ 255 : Remainder = 0
4624 ÷ 4624 : Remainder = 0
3825 ÷ 425 : Remainder = 0
3825 ÷ 765 : Remainder = 0
3825 ÷ 1275 : Remainder = 0
3825 ÷ 3825 : Remainder = 0
Hence, Factors of
4624 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272, 289, 578, 1156, 2312, and 4624
And, Factors of
3825 are 1, 3, 5, 9, 15, 17, 25, 45, 51, 75, 85, 153, 225, 255, 425, 765, 1275, and 3825
Examples of GCF
Sammy baked 4624 chocolate cookies and 3825 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 4624 and 3825.
GCF of 4624 and 3825 is 17.
A class has 4624 boys and 3825 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 4624 and 3825. Hence, GCF of 4624 and 3825 is 17.
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(4624, 3825) = ( 4624 * 3825 ) / LCM(4624, 3825) = 17.
What is the GCF of 4624 and 3825?GCF of 4624 and 3825 is 17.
Ariel is making ready to eat meals to share with friends. She has 4624 bottles of water and 3825 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 4624 and 3825. So the GCF of 4624 and 3825 is 17.
Mary has 4624 blue buttons and 3825 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 4624 and 3825. Hence, the GCF of 4624 and 3825 or the greatest arrangement is 17.
Kamal is making identical balloon arrangements for a party. He has 4624 maroon balloons, and 3825 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 4624 and 3825. So the GCF of 4624 and 3825 is 17.
Kunal is making baskets full of nuts and dried fruits. He has 4624 bags of nuts and 3825 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 4624 and 3825. So the GCF of 4624 and 3825 is 17.