Use our free GCF of Fractions Calculator tool to compute the GCF of 567/612, 714/778 i.e 21/238068 easily. The following is the detailed procedure to determine the greatest common factor of fractions 567/612, 714/778.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 567/612,714/778
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 567/612,714/778, numerators are 567,714
Denominators are 612,778
The GCF of 567,714 is 21 .
LCM of 612,778 is 238068.
The greatest common factor of 567/612,714/778 = [GCF of 567,714]/[LCM of 612,778]= 21/238068
Therefore, the GCF of 567/612,714/778 is 21/238068.
To find the highest common factor of 567,714, we have to find the factors of both numbers and list the highest common factor.
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The HCF of 567,714 is 21.
Lets's calculate GCF of 567,714
3 | 567, 714 |
7 | 189, 238 |
27, 34 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Now, list down the factors of 567
:1,3,7,9,21,27,63,81,189,567
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Greatest Common Factor
We found the factors 567,714 . The biggest common factor number is the GCF number.
So the greatest common factor 567,714 is 21.
Lets's calculate LCM of 612,778
2 | 612, 778 |
306, 389 |
∴ So the LCM of the given numbers is 2 x 306 x 389 = 238068
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/238068
Therefore, the GCF of Fractions 567/612,714/778 is 21/238068
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 612,778 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(612,778) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(612,778) x common factors =2 x 1 = 2
LCM(612,778) = ( 612 × 778 ) / 2
LCM(612,778) = 476136 / 2
LCM(612,778) = 238068
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 567,714?
The HCF of 567,714 is 21
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 567/612, 714/778?
Answer: GCF of Numerators as per given numbers 567/612, 714/778 is
GCF of Numerators i.e. for 567,714 is 21
LCM of denominators i.e. for 612,778 is 238068.
Thus, GCF of Fractions is 21/238068.Finally, GCF of Fractions for 567/612, 714/778 is 21/238068.