Use our free GCF of Fractions Calculator tool to compute the GCF of 29/132, 58/6738 i.e 29/148236 easily. The following is the detailed procedure to determine the greatest common factor of fractions 29/132, 58/6738.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 29/132,58/6738
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 29/132,58/6738, numerators are 29,58
Denominators are 132,6738
The GCF of 29,58 is 29 .
LCM of 132,6738 is 148236.
The greatest common factor of 29/132,58/6738 = [GCF of 29,58]/[LCM of 132,6738]= 29/148236
Therefore, the GCF of 29/132,58/6738 is 29/148236.
To find the highest common factor of 29,58, we have to find the factors of both numbers and list the highest common factor.
The factors of 29 are 1, 29
The factors of 58 are 1, 2, 29, 58
The HCF of 29,58 is 29.
Lets's calculate GCF of 29,58
29 | 29, 58 |
1, 2 |
∴ So the GCF of the given numbers is 29 = 29
Lets's calculate LCM of 132,6738
2 | 132, 6738 |
3 | 66, 3369 |
22, 1123 |
∴ So the LCM of the given numbers is 2 x 3 x 22 x 1123 = 148236
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 29/148236
Therefore, the GCF of Fractions 29/132,58/6738 is 29/148236
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 132,6738 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(132,6738) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(132,6738) x common factors =6 x 1 = 6
LCM(132,6738) = ( 132 × 6738 ) / 6
LCM(132,6738) = 889416 / 6
LCM(132,6738) = 148236
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 29,58?
The HCF of 29,58 is 29
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 29/132, 58/6738?
Answer: GCF of Numerators as per given numbers 29/132, 58/6738 is
GCF of Numerators i.e. for 29,58 is 29
LCM of denominators i.e. for 132,6738 is 148236.
Thus, GCF of Fractions is 29/148236.Finally, GCF of Fractions for 29/132, 58/6738 is 29/148236.