Use our free GCF of Fractions Calculator tool to compute the GCF of 6129/838, 8532/212 i.e 27/88828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6129/838, 8532/212.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 6129/838,8532/212
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 6129/838,8532/212, numerators are 6129,8532
Denominators are 838,212
The GCF of 6129,8532 is 27 .
LCM of 838,212 is 88828.
The greatest common factor of 6129/838,8532/212 = [GCF of 6129,8532]/[LCM of 838,212]= 27/88828
Therefore, the GCF of 6129/838,8532/212 is 27/88828.
To find the highest common factor of 6129,8532, we have to find the factors of both numbers and list the highest common factor.
The factors of 6129 are 1, 3, 9, 27, 227, 681, 2043, 6129
The factors of 8532 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 79, 108, 158, 237, 316, 474, 711, 948, 1422, 2133, 2844, 4266, 8532
The HCF of 6129,8532 is 27.
Lets's calculate GCF of 6129,8532
3 | 6129, 8532 |
3 | 2043, 2844 |
3 | 681, 948 |
227, 316 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Now, list down the factors of 6129
:1,3,9,27,227,681,2043,6129
Now, list down the factors of 8532
:1,2,3,4,6,9,12,18,27,36,54,79,108,158,237,316,474,711,948,1422,2133,2844,4266,8532
Greatest Common Factor
We found the factors 6129,8532 . The biggest common factor number is the GCF number.
So the greatest common factor 6129,8532 is 27.
Lets's calculate LCM of 838,212
2 | 838, 212 |
419, 106 |
∴ So the LCM of the given numbers is 2 x 419 x 106 = 88828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/88828
Therefore, the GCF of Fractions 6129/838,8532/212 is 27/88828
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 838,212 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(838,212) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(838,212) x common factors =2 x 1 = 2
LCM(838,212) = ( 838 × 212 ) / 2
LCM(838,212) = 177656 / 2
LCM(838,212) = 88828
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 6129,8532?
The HCF of 6129,8532 is 27
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 6129/838, 8532/212?
Answer: GCF of Numerators as per given numbers 6129/838, 8532/212 is
GCF of Numerators i.e. for 6129,8532 is 27
LCM of denominators i.e. for 838,212 is 88828.
Thus, GCF of Fractions is 27/88828.Finally, GCF of Fractions for 6129/838, 8532/212 is 27/88828.