GCF of 2082/978, 9716/378
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2082/978, 9716/378 i.e 694/61614 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2082/978, 9716/378.
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 2082/978,9716/378?
Given fractions are 2082/978,9716/378
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 2082/978,9716/378, numerators are 2082,9716
Denominators are 978,378
The GCF of 2082,9716 is 694 .
LCM of 978,378 is 61614.
The greatest common factor of 2082/978,9716/378 = [GCF of 2082,9716]/[LCM of 978,378]= 694/61614
Therefore, the GCF of 2082/978,9716/378 is 694/61614.
To find the highest common factor of 2082,9716, we have to find the factors of both numbers and list the highest common factor.
The factors of 2082 are 1, 2, 3, 6, 347, 694, 1041, 2082
The factors of 9716 are 1, 2, 4, 7, 14, 28, 347, 694, 1388, 2429, 4858, 9716
The HCF of 2082,9716 is 694.
Lets's calculate GCF of 2082,9716
| 2 | 2082, 9716 |
| 347 | 1041, 4858 |
| 3, 14 |
∴ So the GCF of the given numbers is 2 x 347 = 694
Greatest Common Factor of 2082,9716 By Matching Biggest Common Factor Method
Now, list down the factors of 2082
:1,2,3,6,347,694,1041,2082
Now, list down the factors of 9716
:1,2,4,7,14,28,347,694,1388,2429,4858,9716
Greatest Common Factor
We found the factors 2082,9716 . The biggest common factor number is the GCF number.
So the greatest common factor 2082,9716 is 694.
Lets's calculate LCM of 978,378
| 2 | 978, 378 |
| 3 | 489, 189 |
| 163, 63 |
∴ So the LCM of the given numbers is 2 x 3 x 163 x 63 = 61614
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 694/61614
Therefore, the GCF of Fractions 2082/978,9716/378 is 694/61614
Least Common Multiple of 978,378 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 978,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(978,378) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(978,378) x common factors =6 x 1 = 6
LCM(978,378) = ( 978 × 378 ) / 6
LCM(978,378) = 369684 / 6
LCM(978,378) = 61614
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FAQs on GCF of Fractions of 2082/978, 9716/378
1. What is the HCF of 2082,9716?
The HCF of 2082,9716 is 694
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 2082/978, 9716/378?
Answer: GCF of Numerators as per given numbers 2082/978, 9716/378 is
GCF of Numerators i.e. for 2082,9716 is 694
LCM of denominators i.e. for 978,378 is 61614.
Thus, GCF of Fractions is 694/61614.Finally, GCF of Fractions for 2082/978, 9716/378 is 694/61614.