Use our free GCF of Fractions Calculator tool to compute the GCF of 643/612, 971/684 i.e 1/11628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 643/612, 971/684.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 643/612,971/684
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 643/612,971/684, numerators are 643,971
Denominators are 612,684
The GCF of 643,971 is 1 .
LCM of 612,684 is 11628.
The greatest common factor of 643/612,971/684 = [GCF of 643,971]/[LCM of 612,684]= 1/11628
Therefore, the GCF of 643/612,971/684 is 1/11628.
To find the highest common factor of 643,971, we have to find the factors of both numbers and list the highest common factor.
The factors of 643 are 1, 643
The factors of 971 are 1, 971
The HCF of 643,971 is 1.
Lets's calculate GCF of 643,971
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 643
:1,643
Now, list down the factors of 971
:1,971
Greatest Common Factor
We found the factors 643,971 . The biggest common factor number is the GCF number.
So the greatest common factor 643,971 is 1.
Lets's calculate LCM of 612,684
2 | 612, 684 |
2 | 306, 342 |
3 | 153, 171 |
3 | 51, 57 |
17, 19 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 17 x 19 = 11628
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11628
Therefore, the GCF of Fractions 643/612,971/684 is 1/11628
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 612,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(612,684) = 36
common factors(in case of two or more numbers have common factors) = 1
GCF(612,684) x common factors =36 x 1 = 36
LCM(612,684) = ( 612 × 684 ) / 36
LCM(612,684) = 418608 / 36
LCM(612,684) = 11628
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 643,971?
The HCF of 643,971 is 1
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 643/612, 971/684?
Answer: GCF of Numerators as per given numbers 643/612, 971/684 is
GCF of Numerators i.e. for 643,971 is 1
LCM of denominators i.e. for 612,684 is 11628.
Thus, GCF of Fractions is 1/11628.Finally, GCF of Fractions for 643/612, 971/684 is 1/11628.