Use our free GCF of Fractions Calculator tool to compute the GCF of 429/748, 819/342 i.e 39/127908 easily. The following is the detailed procedure to determine the greatest common factor of fractions 429/748, 819/342.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 429/748,819/342
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 429/748,819/342, numerators are 429,819
Denominators are 748,342
The GCF of 429,819 is 39 .
LCM of 748,342 is 127908.
The greatest common factor of 429/748,819/342 = [GCF of 429,819]/[LCM of 748,342]= 39/127908
Therefore, the GCF of 429/748,819/342 is 39/127908.
To find the highest common factor of 429,819, we have to find the factors of both numbers and list the highest common factor.
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The HCF of 429,819 is 39.
Lets's calculate GCF of 429,819
3 | 429, 819 |
13 | 143, 273 |
11, 21 |
∴ So the GCF of the given numbers is 3 x 13 = 39
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Greatest Common Factor
We found the factors 429,819 . The biggest common factor number is the GCF number.
So the greatest common factor 429,819 is 39.
Lets's calculate LCM of 748,342
2 | 748, 342 |
374, 171 |
∴ So the LCM of the given numbers is 2 x 374 x 171 = 127908
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 39/127908
Therefore, the GCF of Fractions 429/748,819/342 is 39/127908
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 748,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(748,342) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(748,342) x common factors =2 x 1 = 2
LCM(748,342) = ( 748 × 342 ) / 2
LCM(748,342) = 255816 / 2
LCM(748,342) = 127908
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 429,819?
The HCF of 429,819 is 39
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 429/748, 819/342?
Answer: GCF of Numerators as per given numbers 429/748, 819/342 is
GCF of Numerators i.e. for 429,819 is 39
LCM of denominators i.e. for 748,342 is 127908.
Thus, GCF of Fractions is 39/127908.Finally, GCF of Fractions for 429/748, 819/342 is 39/127908.