GCF of 59/12, 198/30, 510/317
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 59/12, 198/30, 510/317 i.e 1/19020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 59/12, 198/30, 510/317.
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 59/12,198/30,510/317?
Given fractions are 59/12,198/30,510/317
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 59/12,198/30,510/317, numerators are 59,198,510
Denominators are 12,30,317
The GCF of 59,198,510 is 1 .
LCM of 12,30,317 is 19020.
The greatest common factor of 59/12,198/30,510/317 = [GCF of 59,198,510]/[LCM of 12,30,317]= 1/19020
Therefore, the GCF of 59/12,198/30,510/317 is 1/19020.
To find the highest common factor of 59,198,510, we have to find the factors of both numbers and list the highest common factor.
The factors of 59 are 1, 59
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The HCF of 59,198,510 is 1.
Lets's calculate GCF of 59,198,510
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 59,198,510 By Matching Biggest Common Factor Method
Now, list down the factors of 59
:1,59
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Now, list down the factors of 510
:1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510
Greatest Common Factor
We found the factors 59,198,510 . The biggest common factor number is the GCF number.
So the greatest common factor 59,198,510 is 1.
Lets's calculate LCM of 12,30,317
| 2 | 12, 30, 317 |
| 3 | 6, 15, 317 |
| 2, 5, 317 |
∴ So the LCM of the given numbers is 2 x 3 x 2 x 5 x 317 = 19020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19020
Therefore, the GCF of Fractions 59/12,198/30,510/317 is 1/19020
Least Common Multiple of 12,30,317 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 12,30,317 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,30,317) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(12,30,317) x common factors =1 x 6 = 6
LCM(12,30,317) = ( 12 × 30 × 317 ) / 6
LCM(12,30,317) = 114120 / 6
LCM(12,30,317) = 19020
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FAQs on GCF of Fractions of 59/12, 198/30, 510/317
1. What is the HCF of 59,198,510?
The HCF of 59,198,510 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 59/12, 198/30, 510/317?
Answer: GCF of Numerators as per given numbers 59/12, 198/30, 510/317 is
GCF of Numerators i.e. for 59,198,510 is 1
LCM of denominators i.e. for 12,30,317 is 19020.
Thus, GCF of Fractions is 1/19020.Finally, GCF of Fractions for 59/12, 198/30, 510/317 is 1/19020.