GCF of 7257/583, 8617/1991
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7257/583, 8617/1991 i.e 1/105523 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7257/583, 8617/1991.
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 7257/583,8617/1991?
Given fractions are 7257/583,8617/1991
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 7257/583,8617/1991, numerators are 7257,8617
Denominators are 583,1991
The GCF of 7257,8617 is 1 .
LCM of 583,1991 is 105523.
The greatest common factor of 7257/583,8617/1991 = [GCF of 7257,8617]/[LCM of 583,1991]= 1/105523
Therefore, the GCF of 7257/583,8617/1991 is 1/105523.
To find the highest common factor of 7257,8617, we have to find the factors of both numbers and list the highest common factor.
The factors of 7257 are 1, 3, 41, 59, 123, 177, 2419, 7257
The factors of 8617 are 1, 7, 1231, 8617
The HCF of 7257,8617 is 1.
Lets's calculate GCF of 7257,8617
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7257,8617 By Matching Biggest Common Factor Method
Now, list down the factors of 7257
:1,3,41,59,123,177,2419,7257
Now, list down the factors of 8617
:1,7,1231,8617
Greatest Common Factor
We found the factors 7257,8617 . The biggest common factor number is the GCF number.
So the greatest common factor 7257,8617 is 1.
Lets's calculate LCM of 583,1991
| 11 | 583, 1991 |
| 53, 181 |
∴ So the LCM of the given numbers is 11 x 53 x 181 = 105523
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/105523
Therefore, the GCF of Fractions 7257/583,8617/1991 is 1/105523
Least Common Multiple of 583,1991 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 583,1991 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(583,1991) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(583,1991) x common factors =11 x 1 = 11
LCM(583,1991) = ( 583 × 1991 ) / 11
LCM(583,1991) = 1160753 / 11
LCM(583,1991) = 105523
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FAQs on GCF of Fractions of 7257/583, 8617/1991
1. What is the HCF of 7257,8617?
The HCF of 7257,8617 is 1
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 7257/583, 8617/1991?
Answer: GCF of Numerators as per given numbers 7257/583, 8617/1991 is
GCF of Numerators i.e. for 7257,8617 is 1
LCM of denominators i.e. for 583,1991 is 105523.
Thus, GCF of Fractions is 1/105523.Finally, GCF of Fractions for 7257/583, 8617/1991 is 1/105523.