GCF of 677/398, 546/572
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 677/398, 546/572 i.e 1/113828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 677/398, 546/572.
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 677/398,546/572?
Given fractions are 677/398,546/572
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 677/398,546/572, numerators are 677,546
Denominators are 398,572
The GCF of 677,546 is 1 .
LCM of 398,572 is 113828.
The greatest common factor of 677/398,546/572 = [GCF of 677,546]/[LCM of 398,572]= 1/113828
Therefore, the GCF of 677/398,546/572 is 1/113828.
To find the highest common factor of 677,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 677 are 1, 677
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 677,546 is 1.
Lets's calculate GCF of 677,546
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 677,546 By Matching Biggest Common Factor Method
Now, list down the factors of 677
:1,677
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 677,546 . The biggest common factor number is the GCF number.
So the greatest common factor 677,546 is 1.
Lets's calculate LCM of 398,572
| 2 | 398, 572 |
| 199, 286 |
∴ So the LCM of the given numbers is 2 x 199 x 286 = 113828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/113828
Therefore, the GCF of Fractions 677/398,546/572 is 1/113828
Least Common Multiple of 398,572 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 398,572 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(398,572) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(398,572) x common factors =2 x 1 = 2
LCM(398,572) = ( 398 × 572 ) / 2
LCM(398,572) = 227656 / 2
LCM(398,572) = 113828
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FAQs on GCF of Fractions of 677/398, 546/572
1. What is the HCF of 677,546?
The HCF of 677,546 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 677/398, 546/572?
Answer: GCF of Numerators as per given numbers 677/398, 546/572 is
GCF of Numerators i.e. for 677,546 is 1
LCM of denominators i.e. for 398,572 is 113828.
Thus, GCF of Fractions is 1/113828.Finally, GCF of Fractions for 677/398, 546/572 is 1/113828.