Use our free GCF of Fractions Calculator tool to compute the GCF of 177/202, 834/840 i.e 3/84840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 177/202, 834/840.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 177/202,834/840
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 177/202,834/840, numerators are 177,834
Denominators are 202,840
The GCF of 177,834 is 3 .
LCM of 202,840 is 84840.
The greatest common factor of 177/202,834/840 = [GCF of 177,834]/[LCM of 202,840]= 3/84840
Therefore, the GCF of 177/202,834/840 is 3/84840.
To find the highest common factor of 177,834, we have to find the factors of both numbers and list the highest common factor.
The factors of 177 are 1, 3, 59, 177
The factors of 834 are 1, 2, 3, 6, 139, 278, 417, 834
The HCF of 177,834 is 3.
Lets's calculate GCF of 177,834
3 | 177, 834 |
59, 278 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 177
:1,3,59,177
Now, list down the factors of 834
:1,2,3,6,139,278,417,834
Greatest Common Factor
We found the factors 177,834 . The biggest common factor number is the GCF number.
So the greatest common factor 177,834 is 3.
Lets's calculate LCM of 202,840
2 | 202, 840 |
101, 420 |
∴ So the LCM of the given numbers is 2 x 101 x 420 = 84840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/84840
Therefore, the GCF of Fractions 177/202,834/840 is 3/84840
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 202,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(202,840) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(202,840) x common factors =2 x 1 = 2
LCM(202,840) = ( 202 × 840 ) / 2
LCM(202,840) = 169680 / 2
LCM(202,840) = 84840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 177,834?
The HCF of 177,834 is 3
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 177/202, 834/840?
Answer: GCF of Numerators as per given numbers 177/202, 834/840 is
GCF of Numerators i.e. for 177,834 is 3
LCM of denominators i.e. for 202,840 is 84840.
Thus, GCF of Fractions is 3/84840.Finally, GCF of Fractions for 177/202, 834/840 is 3/84840.