Use our free GCF of Fractions Calculator tool to compute the GCF of 714/381, 6174/423 i.e 42/53721 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/381, 6174/423.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 714/381,6174/423
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 714/381,6174/423, numerators are 714,6174
Denominators are 381,423
The GCF of 714,6174 is 42 .
LCM of 381,423 is 53721.
The greatest common factor of 714/381,6174/423 = [GCF of 714,6174]/[LCM of 381,423]= 42/53721
Therefore, the GCF of 714/381,6174/423 is 42/53721.
To find the highest common factor of 714,6174, we have to find the factors of both numbers and list the highest common factor.
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The factors of 6174 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174
The HCF of 714,6174 is 42.
Lets's calculate GCF of 714,6174
2 | 714, 6174 |
3 | 357, 3087 |
7 | 119, 1029 |
17, 147 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Now, list down the factors of 6174
:1,2,3,6,7,9,14,18,21,42,49,63,98,126,147,294,343,441,686,882,1029,2058,3087,6174
Greatest Common Factor
We found the factors 714,6174 . The biggest common factor number is the GCF number.
So the greatest common factor 714,6174 is 42.
Lets's calculate LCM of 381,423
3 | 381, 423 |
127, 141 |
∴ So the LCM of the given numbers is 3 x 127 x 141 = 53721
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/53721
Therefore, the GCF of Fractions 714/381,6174/423 is 42/53721
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 381,423 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(381,423) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(381,423) x common factors =3 x 1 = 3
LCM(381,423) = ( 381 × 423 ) / 3
LCM(381,423) = 161163 / 3
LCM(381,423) = 53721
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 714,6174?
The HCF of 714,6174 is 42
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 714/381, 6174/423?
Answer: GCF of Numerators as per given numbers 714/381, 6174/423 is
GCF of Numerators i.e. for 714,6174 is 42
LCM of denominators i.e. for 381,423 is 53721.
Thus, GCF of Fractions is 42/53721.Finally, GCF of Fractions for 714/381, 6174/423 is 42/53721.