GCF of 102/190, 614/584
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 102/190, 614/584 i.e 2/55480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 102/190, 614/584.
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 102/190,614/584?
Given fractions are 102/190,614/584
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 102/190,614/584, numerators are 102,614
Denominators are 190,584
The GCF of 102,614 is 2 .
LCM of 190,584 is 55480.
The greatest common factor of 102/190,614/584 = [GCF of 102,614]/[LCM of 190,584]= 2/55480
Therefore, the GCF of 102/190,614/584 is 2/55480.
To find the highest common factor of 102,614, we have to find the factors of both numbers and list the highest common factor.
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The factors of 614 are 1, 2, 307, 614
The HCF of 102,614 is 2.
Lets's calculate GCF of 102,614
| 2 | 102, 614 |
| 51, 307 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 102,614 By Matching Biggest Common Factor Method
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Now, list down the factors of 614
:1,2,307,614
Greatest Common Factor
We found the factors 102,614 . The biggest common factor number is the GCF number.
So the greatest common factor 102,614 is 2.
Lets's calculate LCM of 190,584
| 2 | 190, 584 |
| 95, 292 |
∴ So the LCM of the given numbers is 2 x 95 x 292 = 55480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/55480
Therefore, the GCF of Fractions 102/190,614/584 is 2/55480
Least Common Multiple of 190,584 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 190,584 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(190,584) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(190,584) x common factors =2 x 1 = 2
LCM(190,584) = ( 190 × 584 ) / 2
LCM(190,584) = 110960 / 2
LCM(190,584) = 55480
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FAQs on GCF of Fractions of 102/190, 614/584
1. What is the HCF of 102,614?
The HCF of 102,614 is 2
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 102/190, 614/584?
Answer: GCF of Numerators as per given numbers 102/190, 614/584 is
GCF of Numerators i.e. for 102,614 is 2
LCM of denominators i.e. for 190,584 is 55480.
Thus, GCF of Fractions is 2/55480.Finally, GCF of Fractions for 102/190, 614/584 is 2/55480.