GCF of 986/57, 422/180
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 986/57, 422/180 i.e 2/3420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 986/57, 422/180.
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 986/57,422/180?
Given fractions are 986/57,422/180
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 986/57,422/180, numerators are 986,422
Denominators are 57,180
The GCF of 986,422 is 2 .
LCM of 57,180 is 3420.
The greatest common factor of 986/57,422/180 = [GCF of 986,422]/[LCM of 57,180]= 2/3420
Therefore, the GCF of 986/57,422/180 is 2/3420.
To find the highest common factor of 986,422, we have to find the factors of both numbers and list the highest common factor.
The factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986
The factors of 422 are 1, 2, 211, 422
The HCF of 986,422 is 2.
Lets's calculate GCF of 986,422
| 2 | 986, 422 |
| 493, 211 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 986,422 By Matching Biggest Common Factor Method
Now, list down the factors of 986
:1,2,17,29,34,58,493,986
Now, list down the factors of 422
:1,2,211,422
Greatest Common Factor
We found the factors 986,422 . The biggest common factor number is the GCF number.
So the greatest common factor 986,422 is 2.
Lets's calculate LCM of 57,180
| 3 | 57, 180 |
| 19, 60 |
∴ So the LCM of the given numbers is 3 x 19 x 60 = 3420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3420
Therefore, the GCF of Fractions 986/57,422/180 is 2/3420
Least Common Multiple of 57,180 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 57,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,180) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(57,180) x common factors =3 x 1 = 3
LCM(57,180) = ( 57 × 180 ) / 3
LCM(57,180) = 10260 / 3
LCM(57,180) = 3420
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FAQs on GCF of Fractions of 986/57, 422/180
1. What is the HCF of 986,422?
The HCF of 986,422 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 986/57, 422/180?
Answer: GCF of Numerators as per given numbers 986/57, 422/180 is
GCF of Numerators i.e. for 986,422 is 2
LCM of denominators i.e. for 57,180 is 3420.
Thus, GCF of Fractions is 2/3420.Finally, GCF of Fractions for 986/57, 422/180 is 2/3420.