Use our free GCF of Fractions Calculator tool to compute the GCF of 642/85, 834/3492 i.e 6/296820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 642/85, 834/3492.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 642/85,834/3492
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 642/85,834/3492, numerators are 642,834
Denominators are 85,3492
The GCF of 642,834 is 6 .
LCM of 85,3492 is 296820.
The greatest common factor of 642/85,834/3492 = [GCF of 642,834]/[LCM of 85,3492]= 6/296820
Therefore, the GCF of 642/85,834/3492 is 6/296820.
To find the highest common factor of 642,834, we have to find the factors of both numbers and list the highest common factor.
The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The factors of 834 are 1, 2, 3, 6, 139, 278, 417, 834
The HCF of 642,834 is 6.
Lets's calculate GCF of 642,834
2 | 642, 834 |
3 | 321, 417 |
107, 139 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
Now, list down the factors of 834
:1,2,3,6,139,278,417,834
Greatest Common Factor
We found the factors 642,834 . The biggest common factor number is the GCF number.
So the greatest common factor 642,834 is 6.
Lets's calculate LCM of 85,3492
Given numbers has no common factors except 1. So, there LCM is their product i.e 296820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/296820
Therefore, the GCF of Fractions 642/85,834/3492 is 6/296820
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 85,3492 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,3492) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(85,3492) x common factors =1 x 1 = 1
LCM(85,3492) = ( 85 × 3492 ) / 1
LCM(85,3492) = 296820 / 1
LCM(85,3492) = 296820
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 642,834?
The HCF of 642,834 is 6
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 642/85, 834/3492?
Answer: GCF of Numerators as per given numbers 642/85, 834/3492 is
GCF of Numerators i.e. for 642,834 is 6
LCM of denominators i.e. for 85,3492 is 296820.
Thus, GCF of Fractions is 6/296820.Finally, GCF of Fractions for 642/85, 834/3492 is 6/296820.