Use our free GCF of Fractions Calculator tool to compute the GCF of 61/256, 85/785, 443/414 i.e 1/41598720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/256, 85/785, 443/414.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 61/256,85/785,443/414
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 61/256,85/785,443/414, numerators are 61,85,443
Denominators are 256,785,414
The GCF of 61,85,443 is 1 .
LCM of 256,785,414 is 41598720.
The greatest common factor of 61/256,85/785,443/414 = [GCF of 61,85,443]/[LCM of 256,785,414]= 1/41598720
Therefore, the GCF of 61/256,85/785,443/414 is 1/41598720.
To find the highest common factor of 61,85,443, we have to find the factors of both numbers and list the highest common factor.
The factors of 61 are 1, 61
The factors of 85 are 1, 5, 17, 85
The factors of 443 are 1, 443
The HCF of 61,85,443 is 1.
Lets's calculate GCF of 61,85,443
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 61
:1,61
Now, list down the factors of 85
:1,5,17,85
Now, list down the factors of 443
:1,443
Greatest Common Factor
We found the factors 61,85,443 . The biggest common factor number is the GCF number.
So the greatest common factor 61,85,443 is 1.
Lets's calculate LCM of 256,785,414
2 | 256, 785, 414 |
128, 785, 207 |
∴ So the LCM of the given numbers is 2 x 128 x 785 x 207 = 41598720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41598720
Therefore, the GCF of Fractions 61/256,85/785,443/414 is 1/41598720
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 256,785,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(256,785,414) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(256,785,414) x common factors =1 x 2 = 2
LCM(256,785,414) = ( 256 × 785 × 414 ) / 2
LCM(256,785,414) = 83197440 / 2
LCM(256,785,414) = 41598720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 61,85,443?
The HCF of 61,85,443 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 61/256, 85/785, 443/414?
Answer: GCF of Numerators as per given numbers 61/256, 85/785, 443/414 is
GCF of Numerators i.e. for 61,85,443 is 1
LCM of denominators i.e. for 256,785,414 is 41598720.
Thus, GCF of Fractions is 1/41598720.Finally, GCF of Fractions for 61/256, 85/785, 443/414 is 1/41598720.