GCF of 769/686, 314/104
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 769/686, 314/104 i.e 1/35672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 769/686, 314/104.
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 769/686,314/104?
Given fractions are 769/686,314/104
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 769/686,314/104, numerators are 769,314
Denominators are 686,104
The GCF of 769,314 is 1 .
LCM of 686,104 is 35672.
The greatest common factor of 769/686,314/104 = [GCF of 769,314]/[LCM of 686,104]= 1/35672
Therefore, the GCF of 769/686,314/104 is 1/35672.
To find the highest common factor of 769,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 769 are 1, 769
The factors of 314 are 1, 2, 157, 314
The HCF of 769,314 is 1.
Lets's calculate GCF of 769,314
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 769,314 By Matching Biggest Common Factor Method
Now, list down the factors of 769
:1,769
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 769,314 . The biggest common factor number is the GCF number.
So the greatest common factor 769,314 is 1.
Lets's calculate LCM of 686,104
| 2 | 686, 104 |
| 343, 52 |
∴ So the LCM of the given numbers is 2 x 343 x 52 = 35672
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/35672
Therefore, the GCF of Fractions 769/686,314/104 is 1/35672
Least Common Multiple of 686,104 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 686,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(686,104) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(686,104) x common factors =2 x 1 = 2
LCM(686,104) = ( 686 × 104 ) / 2
LCM(686,104) = 71344 / 2
LCM(686,104) = 35672
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FAQs on GCF of Fractions of 769/686, 314/104
1. What is the HCF of 769,314?
The HCF of 769,314 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 769/686, 314/104?
Answer: GCF of Numerators as per given numbers 769/686, 314/104 is
GCF of Numerators i.e. for 769,314 is 1
LCM of denominators i.e. for 686,104 is 35672.
Thus, GCF of Fractions is 1/35672.Finally, GCF of Fractions for 769/686, 314/104 is 1/35672.