GCF of 314/77, 986/935
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 314/77, 986/935 i.e 2/6545 easily. The following is the detailed procedure to determine the greatest common factor of fractions 314/77, 986/935.
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 314/77,986/935?
Given fractions are 314/77,986/935
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 314/77,986/935, numerators are 314,986
Denominators are 77,935
The GCF of 314,986 is 2 .
LCM of 77,935 is 6545.
The greatest common factor of 314/77,986/935 = [GCF of 314,986]/[LCM of 77,935]= 2/6545
Therefore, the GCF of 314/77,986/935 is 2/6545.
To find the highest common factor of 314,986, we have to find the factors of both numbers and list the highest common factor.
The factors of 314 are 1, 2, 157, 314
The factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986
The HCF of 314,986 is 2.
Lets's calculate GCF of 314,986
| 2 | 314, 986 |
| 157, 493 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 314,986 By Matching Biggest Common Factor Method
Now, list down the factors of 314
:1,2,157,314
Now, list down the factors of 986
:1,2,17,29,34,58,493,986
Greatest Common Factor
We found the factors 314,986 . The biggest common factor number is the GCF number.
So the greatest common factor 314,986 is 2.
Lets's calculate LCM of 77,935
| 11 | 77, 935 |
| 7, 85 |
∴ So the LCM of the given numbers is 11 x 7 x 85 = 6545
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6545
Therefore, the GCF of Fractions 314/77,986/935 is 2/6545
Least Common Multiple of 77,935 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 77,935 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,935) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(77,935) x common factors =11 x 1 = 11
LCM(77,935) = ( 77 × 935 ) / 11
LCM(77,935) = 71995 / 11
LCM(77,935) = 6545
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FAQs on GCF of Fractions of 314/77, 986/935
1. What is the HCF of 314,986?
The HCF of 314,986 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 314/77, 986/935?
Answer: GCF of Numerators as per given numbers 314/77, 986/935 is
GCF of Numerators i.e. for 314,986 is 2
LCM of denominators i.e. for 77,935 is 6545.
Thus, GCF of Fractions is 2/6545.Finally, GCF of Fractions for 314/77, 986/935 is 2/6545.