GCF of 517/30, 188/574
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 517/30, 188/574 i.e 47/8610 easily. The following is the detailed procedure to determine the greatest common factor of fractions 517/30, 188/574.
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 517/30,188/574?
Given fractions are 517/30,188/574
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 517/30,188/574, numerators are 517,188
Denominators are 30,574
The GCF of 517,188 is 47 .
LCM of 30,574 is 8610.
The greatest common factor of 517/30,188/574 = [GCF of 517,188]/[LCM of 30,574]= 47/8610
Therefore, the GCF of 517/30,188/574 is 47/8610.
To find the highest common factor of 517,188, we have to find the factors of both numbers and list the highest common factor.
The factors of 517 are 1, 11, 47, 517
The factors of 188 are 1, 2, 4, 47, 94, 188
The HCF of 517,188 is 47.
Lets's calculate GCF of 517,188
| 47 | 517, 188 |
| 11, 4 |
∴ So the GCF of the given numbers is 47 = 47
Greatest Common Factor of 517,188 By Matching Biggest Common Factor Method
Now, list down the factors of 517
:1,11,47,517
Now, list down the factors of 188
:1,2,4,47,94,188
Greatest Common Factor
We found the factors 517,188 . The biggest common factor number is the GCF number.
So the greatest common factor 517,188 is 47.
Lets's calculate LCM of 30,574
| 2 | 30, 574 |
| 15, 287 |
∴ So the LCM of the given numbers is 2 x 15 x 287 = 8610
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 47/8610
Therefore, the GCF of Fractions 517/30,188/574 is 47/8610
Least Common Multiple of 30,574 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 30,574 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,574) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(30,574) x common factors =2 x 1 = 2
LCM(30,574) = ( 30 × 574 ) / 2
LCM(30,574) = 17220 / 2
LCM(30,574) = 8610
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FAQs on GCF of Fractions of 517/30, 188/574
1. What is the HCF of 517,188?
The HCF of 517,188 is 47
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 517/30, 188/574?
Answer: GCF of Numerators as per given numbers 517/30, 188/574 is
GCF of Numerators i.e. for 517,188 is 47
LCM of denominators i.e. for 30,574 is 8610.
Thus, GCF of Fractions is 47/8610.Finally, GCF of Fractions for 517/30, 188/574 is 47/8610.