Use our free GCF of Fractions Calculator tool to compute the GCF of 419/932, 749/840 i.e 1/195720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 419/932, 749/840.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 419/932,749/840
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 419/932,749/840, numerators are 419,749
Denominators are 932,840
The GCF of 419,749 is 1 .
LCM of 932,840 is 195720.
The greatest common factor of 419/932,749/840 = [GCF of 419,749]/[LCM of 932,840]= 1/195720
Therefore, the GCF of 419/932,749/840 is 1/195720.
To find the highest common factor of 419,749, we have to find the factors of both numbers and list the highest common factor.
The factors of 419 are 1, 419
The factors of 749 are 1, 7, 107, 749
The HCF of 419,749 is 1.
Lets's calculate GCF of 419,749
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 419
:1,419
Now, list down the factors of 749
:1,7,107,749
Greatest Common Factor
We found the factors 419,749 . The biggest common factor number is the GCF number.
So the greatest common factor 419,749 is 1.
Lets's calculate LCM of 932,840
2 | 932, 840 |
2 | 466, 420 |
233, 210 |
∴ So the LCM of the given numbers is 2 x 2 x 233 x 210 = 195720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/195720
Therefore, the GCF of Fractions 419/932,749/840 is 1/195720
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 932,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(932,840) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(932,840) x common factors =4 x 1 = 4
LCM(932,840) = ( 932 × 840 ) / 4
LCM(932,840) = 782880 / 4
LCM(932,840) = 195720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 419,749?
The HCF of 419,749 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 419/932, 749/840?
Answer: GCF of Numerators as per given numbers 419/932, 749/840 is
GCF of Numerators i.e. for 419,749 is 1
LCM of denominators i.e. for 932,840 is 195720.
Thus, GCF of Fractions is 1/195720.Finally, GCF of Fractions for 419/932, 749/840 is 1/195720.