GCF of 580/77, 931/217
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 580/77, 931/217 i.e 1/2387 easily. The following is the detailed procedure to determine the greatest common factor of fractions 580/77, 931/217.
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 580/77,931/217?
Given fractions are 580/77,931/217
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 580/77,931/217, numerators are 580,931
Denominators are 77,217
The GCF of 580,931 is 1 .
LCM of 77,217 is 2387.
The greatest common factor of 580/77,931/217 = [GCF of 580,931]/[LCM of 77,217]= 1/2387
Therefore, the GCF of 580/77,931/217 is 1/2387.
To find the highest common factor of 580,931, we have to find the factors of both numbers and list the highest common factor.
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The factors of 931 are 1, 7, 19, 49, 133, 931
The HCF of 580,931 is 1.
Lets's calculate GCF of 580,931
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 580,931 By Matching Biggest Common Factor Method
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Now, list down the factors of 931
:1,7,19,49,133,931
Greatest Common Factor
We found the factors 580,931 . The biggest common factor number is the GCF number.
So the greatest common factor 580,931 is 1.
Lets's calculate LCM of 77,217
| 7 | 77, 217 |
| 11, 31 |
∴ So the LCM of the given numbers is 7 x 11 x 31 = 2387
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2387
Therefore, the GCF of Fractions 580/77,931/217 is 1/2387
Least Common Multiple of 77,217 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 77,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,217) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(77,217) x common factors =7 x 1 = 7
LCM(77,217) = ( 77 × 217 ) / 7
LCM(77,217) = 16709 / 7
LCM(77,217) = 2387
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FAQs on GCF of Fractions of 580/77, 931/217
1. What is the HCF of 580,931?
The HCF of 580,931 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 580/77, 931/217?
Answer: GCF of Numerators as per given numbers 580/77, 931/217 is
GCF of Numerators i.e. for 580,931 is 1
LCM of denominators i.e. for 77,217 is 2387.
Thus, GCF of Fractions is 1/2387.Finally, GCF of Fractions for 580/77, 931/217 is 1/2387.