Use our free GCF of Fractions Calculator tool to compute the GCF of 13/274, 57/682 i.e 1/93434 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/274, 57/682.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 13/274,57/682
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 13/274,57/682, numerators are 13,57
Denominators are 274,682
The GCF of 13,57 is 1 .
LCM of 274,682 is 93434.
The greatest common factor of 13/274,57/682 = [GCF of 13,57]/[LCM of 274,682]= 1/93434
Therefore, the GCF of 13/274,57/682 is 1/93434.
To find the highest common factor of 13,57, we have to find the factors of both numbers and list the highest common factor.
The factors of 13 are 1, 13
The factors of 57 are 1, 3, 19, 57
The HCF of 13,57 is 1.
Lets's calculate GCF of 13,57
∴ So GCF of numbers is 1 because of no common factors present between them.
Lets's calculate LCM of 274,682
2 | 274, 682 |
137, 341 |
∴ So the LCM of the given numbers is 2 x 137 x 341 = 93434
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/93434
Therefore, the GCF of Fractions 13/274,57/682 is 1/93434
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 274,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(274,682) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(274,682) x common factors =2 x 1 = 2
LCM(274,682) = ( 274 × 682 ) / 2
LCM(274,682) = 186868 / 2
LCM(274,682) = 93434
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 13,57?
The HCF of 13,57 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 13/274, 57/682?
Answer: GCF of Numerators as per given numbers 13/274, 57/682 is
GCF of Numerators i.e. for 13,57 is 1
LCM of denominators i.e. for 274,682 is 93434.
Thus, GCF of Fractions is 1/93434.Finally, GCF of Fractions for 13/274, 57/682 is 1/93434.