GCF of 654/458, 677/687
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 654/458, 677/687 i.e 1/1374 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/458, 677/687.
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 654/458,677/687?
Given fractions are 654/458,677/687
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 654/458,677/687, numerators are 654,677
Denominators are 458,687
The GCF of 654,677 is 1 .
LCM of 458,687 is 1374.
The greatest common factor of 654/458,677/687 = [GCF of 654,677]/[LCM of 458,687]= 1/1374
Therefore, the GCF of 654/458,677/687 is 1/1374.
To find the highest common factor of 654,677, we have to find the factors of both numbers and list the highest common factor.
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The factors of 677 are 1, 677
The HCF of 654,677 is 1.
Lets's calculate GCF of 654,677
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 654,677 By Matching Biggest Common Factor Method
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Now, list down the factors of 677
:1,677
Greatest Common Factor
We found the factors 654,677 . The biggest common factor number is the GCF number.
So the greatest common factor 654,677 is 1.
Lets's calculate LCM of 458,687
| 229 | 458, 687 |
| 2, 3 |
∴ So the LCM of the given numbers is 229 x 2 x 3 = 1374
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1374
Therefore, the GCF of Fractions 654/458,677/687 is 1/1374
Least Common Multiple of 458,687 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 458,687 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(458,687) = 229
common factors(in case of two or more numbers have common factors) = 1
GCF(458,687) x common factors =229 x 1 = 229
LCM(458,687) = ( 458 × 687 ) / 229
LCM(458,687) = 314646 / 229
LCM(458,687) = 1374
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 654/458, 677/687
1. What is the HCF of 654,677?
The HCF of 654,677 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 654/458, 677/687?
Answer: GCF of Numerators as per given numbers 654/458, 677/687 is
GCF of Numerators i.e. for 654,677 is 1
LCM of denominators i.e. for 458,687 is 1374.
Thus, GCF of Fractions is 1/1374.Finally, GCF of Fractions for 654/458, 677/687 is 1/1374.