GCF of 680/54, 766/2978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 680/54, 766/2978 i.e 2/80406 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/54, 766/2978.
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 680/54,766/2978?
Given fractions are 680/54,766/2978
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 680/54,766/2978, numerators are 680,766
Denominators are 54,2978
The GCF of 680,766 is 2 .
LCM of 54,2978 is 80406.
The greatest common factor of 680/54,766/2978 = [GCF of 680,766]/[LCM of 54,2978]= 2/80406
Therefore, the GCF of 680/54,766/2978 is 2/80406.
To find the highest common factor of 680,766, we have to find the factors of both numbers and list the highest common factor.
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The factors of 766 are 1, 2, 383, 766
The HCF of 680,766 is 2.
Lets's calculate GCF of 680,766
| 2 | 680, 766 |
| 340, 383 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 680,766 By Matching Biggest Common Factor Method
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Now, list down the factors of 766
:1,2,383,766
Greatest Common Factor
We found the factors 680,766 . The biggest common factor number is the GCF number.
So the greatest common factor 680,766 is 2.
Lets's calculate LCM of 54,2978
| 2 | 54, 2978 |
| 27, 1489 |
∴ So the LCM of the given numbers is 2 x 27 x 1489 = 80406
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/80406
Therefore, the GCF of Fractions 680/54,766/2978 is 2/80406
Least Common Multiple of 54,2978 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 54,2978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,2978) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,2978) x common factors =2 x 1 = 2
LCM(54,2978) = ( 54 × 2978 ) / 2
LCM(54,2978) = 160812 / 2
LCM(54,2978) = 80406
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FAQs on GCF of Fractions of 680/54, 766/2978
1. What is the HCF of 680,766?
The HCF of 680,766 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 680/54, 766/2978?
Answer: GCF of Numerators as per given numbers 680/54, 766/2978 is
GCF of Numerators i.e. for 680,766 is 2
LCM of denominators i.e. for 54,2978 is 80406.
Thus, GCF of Fractions is 2/80406.Finally, GCF of Fractions for 680/54, 766/2978 is 2/80406.