Use our free GCF of Fractions Calculator tool to compute the GCF of 654/412, 977/344 i.e 1/35432 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/412, 977/344.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 654/412,977/344
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 654/412,977/344, numerators are 654,977
Denominators are 412,344
The GCF of 654,977 is 1 .
LCM of 412,344 is 35432.
The greatest common factor of 654/412,977/344 = [GCF of 654,977]/[LCM of 412,344]= 1/35432
Therefore, the GCF of 654/412,977/344 is 1/35432.
To find the highest common factor of 654,977, we have to find the factors of both numbers and list the highest common factor.
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The factors of 977 are 1, 977
The HCF of 654,977 is 1.
Lets's calculate GCF of 654,977
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Now, list down the factors of 977
:1,977
Greatest Common Factor
We found the factors 654,977 . The biggest common factor number is the GCF number.
So the greatest common factor 654,977 is 1.
Lets's calculate LCM of 412,344
2 | 412, 344 |
2 | 206, 172 |
103, 86 |
∴ So the LCM of the given numbers is 2 x 2 x 103 x 86 = 35432
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/35432
Therefore, the GCF of Fractions 654/412,977/344 is 1/35432
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 412,344 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(412,344) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(412,344) x common factors =4 x 1 = 4
LCM(412,344) = ( 412 × 344 ) / 4
LCM(412,344) = 141728 / 4
LCM(412,344) = 35432
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 654,977?
The HCF of 654,977 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 654/412, 977/344?
Answer: GCF of Numerators as per given numbers 654/412, 977/344 is
GCF of Numerators i.e. for 654,977 is 1
LCM of denominators i.e. for 412,344 is 35432.
Thus, GCF of Fractions is 1/35432.Finally, GCF of Fractions for 654/412, 977/344 is 1/35432.