Use our free GCF of Fractions Calculator tool to compute the GCF of 423/257, 709/874 i.e 1/224618 easily. The following is the detailed procedure to determine the greatest common factor of fractions 423/257, 709/874.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 423/257,709/874
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 423/257,709/874, numerators are 423,709
Denominators are 257,874
The GCF of 423,709 is 1 .
LCM of 257,874 is 224618.
The greatest common factor of 423/257,709/874 = [GCF of 423,709]/[LCM of 257,874]= 1/224618
Therefore, the GCF of 423/257,709/874 is 1/224618.
To find the highest common factor of 423,709, we have to find the factors of both numbers and list the highest common factor.
The factors of 423 are 1, 3, 9, 47, 141, 423
The factors of 709 are 1, 709
The HCF of 423,709 is 1.
Lets's calculate GCF of 423,709
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 423
:1,3,9,47,141,423
Now, list down the factors of 709
:1,709
Greatest Common Factor
We found the factors 423,709 . The biggest common factor number is the GCF number.
So the greatest common factor 423,709 is 1.
Lets's calculate LCM of 257,874
Given numbers has no common factors except 1. So, there LCM is their product i.e 224618
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/224618
Therefore, the GCF of Fractions 423/257,709/874 is 1/224618
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 257,874 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(257,874) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(257,874) x common factors =1 x 1 = 1
LCM(257,874) = ( 257 × 874 ) / 1
LCM(257,874) = 224618 / 1
LCM(257,874) = 224618
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 423,709?
The HCF of 423,709 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 423/257, 709/874?
Answer: GCF of Numerators as per given numbers 423/257, 709/874 is
GCF of Numerators i.e. for 423,709 is 1
LCM of denominators i.e. for 257,874 is 224618.
Thus, GCF of Fractions is 1/224618.Finally, GCF of Fractions for 423/257, 709/874 is 1/224618.