GCF of 814/51, 259/3687
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 814/51, 259/3687 i.e 37/62679 easily. The following is the detailed procedure to determine the greatest common factor of fractions 814/51, 259/3687.
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 814/51,259/3687?
Given fractions are 814/51,259/3687
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 814/51,259/3687, numerators are 814,259
Denominators are 51,3687
The GCF of 814,259 is 37 .
LCM of 51,3687 is 62679.
The greatest common factor of 814/51,259/3687 = [GCF of 814,259]/[LCM of 51,3687]= 37/62679
Therefore, the GCF of 814/51,259/3687 is 37/62679.
To find the highest common factor of 814,259, we have to find the factors of both numbers and list the highest common factor.
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The factors of 259 are 1, 7, 37, 259
The HCF of 814,259 is 37.
Lets's calculate GCF of 814,259
| 37 | 814, 259 |
| 22, 7 |
∴ So the GCF of the given numbers is 37 = 37
Greatest Common Factor of 814,259 By Matching Biggest Common Factor Method
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Now, list down the factors of 259
:1,7,37,259
Greatest Common Factor
We found the factors 814,259 . The biggest common factor number is the GCF number.
So the greatest common factor 814,259 is 37.
Lets's calculate LCM of 51,3687
| 3 | 51, 3687 |
| 17, 1229 |
∴ So the LCM of the given numbers is 3 x 17 x 1229 = 62679
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 37/62679
Therefore, the GCF of Fractions 814/51,259/3687 is 37/62679
Least Common Multiple of 51,3687 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 51,3687 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,3687) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(51,3687) x common factors =3 x 1 = 3
LCM(51,3687) = ( 51 × 3687 ) / 3
LCM(51,3687) = 188037 / 3
LCM(51,3687) = 62679
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FAQs on GCF of Fractions of 814/51, 259/3687
1. What is the HCF of 814,259?
The HCF of 814,259 is 37
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 814/51, 259/3687?
Answer: GCF of Numerators as per given numbers 814/51, 259/3687 is
GCF of Numerators i.e. for 814,259 is 37
LCM of denominators i.e. for 51,3687 is 62679.
Thus, GCF of Fractions is 37/62679.Finally, GCF of Fractions for 814/51, 259/3687 is 37/62679.