GCF of 8125/289, 6125/1307
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8125/289, 6125/1307 i.e 125/377723 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8125/289, 6125/1307.
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 8125/289,6125/1307?
Given fractions are 8125/289,6125/1307
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 8125/289,6125/1307, numerators are 8125,6125
Denominators are 289,1307
The GCF of 8125,6125 is 125 .
LCM of 289,1307 is 377723.
The greatest common factor of 8125/289,6125/1307 = [GCF of 8125,6125]/[LCM of 289,1307]= 125/377723
Therefore, the GCF of 8125/289,6125/1307 is 125/377723.
To find the highest common factor of 8125,6125, we have to find the factors of both numbers and list the highest common factor.
The factors of 8125 are 1, 5, 13, 25, 65, 125, 325, 625, 1625, 8125
The factors of 6125 are 1, 5, 7, 25, 35, 49, 125, 175, 245, 875, 1225, 6125
The HCF of 8125,6125 is 125.
Lets's calculate GCF of 8125,6125
| 5 | 8125, 6125 |
| 5 | 1625, 1225 |
| 5 | 325, 245 |
| 65, 49 |
∴ So the GCF of the given numbers is 5 x 5 x 5 = 125
Greatest Common Factor of 8125,6125 By Matching Biggest Common Factor Method
Now, list down the factors of 8125
:1,5,13,25,65,125,325,625,1625,8125
Now, list down the factors of 6125
:1,5,7,25,35,49,125,175,245,875,1225,6125
Greatest Common Factor
We found the factors 8125,6125 . The biggest common factor number is the GCF number.
So the greatest common factor 8125,6125 is 125.
Lets's calculate LCM of 289,1307
Given numbers has no common factors except 1. So, there LCM is their product i.e 377723
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 125/377723
Therefore, the GCF of Fractions 8125/289,6125/1307 is 125/377723
Least Common Multiple of 289,1307 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 289,1307 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,1307) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(289,1307) x common factors =1 x 1 = 1
LCM(289,1307) = ( 289 × 1307 ) / 1
LCM(289,1307) = 377723 / 1
LCM(289,1307) = 377723
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FAQs on GCF of Fractions of 8125/289, 6125/1307
1. What is the HCF of 8125,6125?
The HCF of 8125,6125 is 125
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 8125/289, 6125/1307?
Answer: GCF of Numerators as per given numbers 8125/289, 6125/1307 is
GCF of Numerators i.e. for 8125,6125 is 125
LCM of denominators i.e. for 289,1307 is 377723.
Thus, GCF of Fractions is 125/377723.Finally, GCF of Fractions for 8125/289, 6125/1307 is 125/377723.