Use our free GCF of Fractions Calculator tool to compute the GCF of 34/596, 103/213, 172/682 i.e 1/43289268 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/596, 103/213, 172/682.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 34/596,103/213,172/682
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 34/596,103/213,172/682, numerators are 34,103,172
Denominators are 596,213,682
The GCF of 34,103,172 is 1 .
LCM of 596,213,682 is 43289268.
The greatest common factor of 34/596,103/213,172/682 = [GCF of 34,103,172]/[LCM of 596,213,682]= 1/43289268
Therefore, the GCF of 34/596,103/213,172/682 is 1/43289268.
To find the highest common factor of 34,103,172, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 103 are 1, 103
The factors of 172 are 1, 2, 4, 43, 86, 172
The HCF of 34,103,172 is 1.
Lets's calculate GCF of 34,103,172
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 103
:1,103
Now, list down the factors of 172
:1,2,4,43,86,172
Greatest Common Factor
We found the factors 34,103,172 . The biggest common factor number is the GCF number.
So the greatest common factor 34,103,172 is 1.
Lets's calculate LCM of 596,213,682
2 | 596, 213, 682 |
298, 213, 341 |
∴ So the LCM of the given numbers is 2 x 298 x 213 x 341 = 43289268
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43289268
Therefore, the GCF of Fractions 34/596,103/213,172/682 is 1/43289268
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 596,213,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(596,213,682) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(596,213,682) x common factors =1 x 2 = 2
LCM(596,213,682) = ( 596 × 213 × 682 ) / 2
LCM(596,213,682) = 86578536 / 2
LCM(596,213,682) = 43289268
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 34,103,172?
The HCF of 34,103,172 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 34/596, 103/213, 172/682?
Answer: GCF of Numerators as per given numbers 34/596, 103/213, 172/682 is
GCF of Numerators i.e. for 34,103,172 is 1
LCM of denominators i.e. for 596,213,682 is 43289268.
Thus, GCF of Fractions is 1/43289268.Finally, GCF of Fractions for 34/596, 103/213, 172/682 is 1/43289268.