GCF of 6102/734, 7725/8514
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6102/734, 7725/8514 i.e 3/3124638 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6102/734, 7725/8514.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 6102/734,7725/8514?
Given fractions are 6102/734,7725/8514
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 6102/734,7725/8514, numerators are 6102,7725
Denominators are 734,8514
The GCF of 6102,7725 is 3 .
LCM of 734,8514 is 3124638.
The greatest common factor of 6102/734,7725/8514 = [GCF of 6102,7725]/[LCM of 734,8514]= 3/3124638
Therefore, the GCF of 6102/734,7725/8514 is 3/3124638.
To find the highest common factor of 6102,7725, we have to find the factors of both numbers and list the highest common factor.
The factors of 6102 are 1, 2, 3, 6, 9, 18, 27, 54, 113, 226, 339, 678, 1017, 2034, 3051, 6102
The factors of 7725 are 1, 3, 5, 15, 25, 75, 103, 309, 515, 1545, 2575, 7725
The HCF of 6102,7725 is 3.
Lets's calculate GCF of 6102,7725
| 3 | 6102, 7725 |
| 2034, 2575 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 6102,7725 By Matching Biggest Common Factor Method
Now, list down the factors of 6102
:1,2,3,6,9,18,27,54,113,226,339,678,1017,2034,3051,6102
Now, list down the factors of 7725
:1,3,5,15,25,75,103,309,515,1545,2575,7725
Greatest Common Factor
We found the factors 6102,7725 . The biggest common factor number is the GCF number.
So the greatest common factor 6102,7725 is 3.
Lets's calculate LCM of 734,8514
| 2 | 734, 8514 |
| 367, 4257 |
∴ So the LCM of the given numbers is 2 x 367 x 4257 = 3124638
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3124638
Therefore, the GCF of Fractions 6102/734,7725/8514 is 3/3124638
Least Common Multiple of 734,8514 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 734,8514 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(734,8514) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(734,8514) x common factors =2 x 1 = 2
LCM(734,8514) = ( 734 × 8514 ) / 2
LCM(734,8514) = 6249276 / 2
LCM(734,8514) = 3124638
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FAQs on GCF of Fractions of 6102/734, 7725/8514
1. What is the HCF of 6102,7725?
The HCF of 6102,7725 is 3
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 6102/734, 7725/8514?
Answer: GCF of Numerators as per given numbers 6102/734, 7725/8514 is
GCF of Numerators i.e. for 6102,7725 is 3
LCM of denominators i.e. for 734,8514 is 3124638.
Thus, GCF of Fractions is 3/3124638.Finally, GCF of Fractions for 6102/734, 7725/8514 is 3/3124638.