Use our free GCF of Fractions Calculator tool to compute the GCF of 61/284, 659/322, 689/254 i.e 1/5806948 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/284, 659/322, 689/254.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 61/284,659/322,689/254
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 61/284,659/322,689/254, numerators are 61,659,689
Denominators are 284,322,254
The GCF of 61,659,689 is 1 .
LCM of 284,322,254 is 5806948.
The greatest common factor of 61/284,659/322,689/254 = [GCF of 61,659,689]/[LCM of 284,322,254]= 1/5806948
Therefore, the GCF of 61/284,659/322,689/254 is 1/5806948.
To find the highest common factor of 61,659,689, 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 659 are 1, 659
The factors of 689 are 1, 13, 53, 689
The HCF of 61,659,689 is 1.
Lets's calculate GCF of 61,659,689
∴ 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 659
:1,659
Now, list down the factors of 689
:1,13,53,689
Greatest Common Factor
We found the factors 61,659,689 . The biggest common factor number is the GCF number.
So the greatest common factor 61,659,689 is 1.
Lets's calculate LCM of 284,322,254
2 | 284, 322, 254 |
142, 161, 127 |
∴ So the LCM of the given numbers is 2 x 142 x 161 x 127 = 5806948
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5806948
Therefore, the GCF of Fractions 61/284,659/322,689/254 is 1/5806948
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 284,322,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(284,322,254) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(284,322,254) x common factors =2 x 2 = 4
LCM(284,322,254) = ( 284 × 322 × 254 ) / 4
LCM(284,322,254) = 23227792 / 4
LCM(284,322,254) = 5806948
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 61,659,689?
The HCF of 61,659,689 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 61/284, 659/322, 689/254?
Answer: GCF of Numerators as per given numbers 61/284, 659/322, 689/254 is
GCF of Numerators i.e. for 61,659,689 is 1
LCM of denominators i.e. for 284,322,254 is 5806948.
Thus, GCF of Fractions is 1/5806948.Finally, GCF of Fractions for 61/284, 659/322, 689/254 is 1/5806948.