Use our free GCF of Fractions Calculator tool to compute the GCF of 707/346, 1728/3268 i.e 1/565364 easily. The following is the detailed procedure to determine the greatest common factor of fractions 707/346, 1728/3268.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 707/346,1728/3268
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 707/346,1728/3268, numerators are 707,1728
Denominators are 346,3268
The GCF of 707,1728 is 1 .
LCM of 346,3268 is 565364.
The greatest common factor of 707/346,1728/3268 = [GCF of 707,1728]/[LCM of 346,3268]= 1/565364
Therefore, the GCF of 707/346,1728/3268 is 1/565364.
To find the highest common factor of 707,1728, we have to find the factors of both numbers and list the highest common factor.
The factors of 707 are 1, 7, 101, 707
The factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728
The HCF of 707,1728 is 1.
Lets's calculate GCF of 707,1728
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 707
:1,7,101,707
Now, list down the factors of 1728
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,144,192,216,288,432,576,864,1728
Greatest Common Factor
We found the factors 707,1728 . The biggest common factor number is the GCF number.
So the greatest common factor 707,1728 is 1.
Lets's calculate LCM of 346,3268
2 | 346, 3268 |
173, 1634 |
∴ So the LCM of the given numbers is 2 x 173 x 1634 = 565364
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/565364
Therefore, the GCF of Fractions 707/346,1728/3268 is 1/565364
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 346,3268 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(346,3268) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(346,3268) x common factors =2 x 1 = 2
LCM(346,3268) = ( 346 × 3268 ) / 2
LCM(346,3268) = 1130728 / 2
LCM(346,3268) = 565364
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 707,1728?
The HCF of 707,1728 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 707/346, 1728/3268?
Answer: GCF of Numerators as per given numbers 707/346, 1728/3268 is
GCF of Numerators i.e. for 707,1728 is 1
LCM of denominators i.e. for 346,3268 is 565364.
Thus, GCF of Fractions is 1/565364.Finally, GCF of Fractions for 707/346, 1728/3268 is 1/565364.