Use our free GCF of Fractions Calculator tool to compute the GCF of 472/706, 328/214 i.e 8/75542 easily. The following is the detailed procedure to determine the greatest common factor of fractions 472/706, 328/214.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 472/706,328/214
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 472/706,328/214, numerators are 472,328
Denominators are 706,214
The GCF of 472,328 is 8 .
LCM of 706,214 is 75542.
The greatest common factor of 472/706,328/214 = [GCF of 472,328]/[LCM of 706,214]= 8/75542
Therefore, the GCF of 472/706,328/214 is 8/75542.
To find the highest common factor of 472,328, we have to find the factors of both numbers and list the highest common factor.
The factors of 472 are 1, 2, 4, 8, 59, 118, 236, 472
The factors of 328 are 1, 2, 4, 8, 41, 82, 164, 328
The HCF of 472,328 is 8.
Lets's calculate GCF of 472,328
2 | 472, 328 |
2 | 236, 164 |
2 | 118, 82 |
59, 41 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 472
:1,2,4,8,59,118,236,472
Now, list down the factors of 328
:1,2,4,8,41,82,164,328
Greatest Common Factor
We found the factors 472,328 . The biggest common factor number is the GCF number.
So the greatest common factor 472,328 is 8.
Lets's calculate LCM of 706,214
2 | 706, 214 |
353, 107 |
∴ So the LCM of the given numbers is 2 x 353 x 107 = 75542
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/75542
Therefore, the GCF of Fractions 472/706,328/214 is 8/75542
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 706,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(706,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(706,214) x common factors =2 x 1 = 2
LCM(706,214) = ( 706 × 214 ) / 2
LCM(706,214) = 151084 / 2
LCM(706,214) = 75542
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 472,328?
The HCF of 472,328 is 8
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 472/706, 328/214?
Answer: GCF of Numerators as per given numbers 472/706, 328/214 is
GCF of Numerators i.e. for 472,328 is 8
LCM of denominators i.e. for 706,214 is 75542.
Thus, GCF of Fractions is 8/75542.Finally, GCF of Fractions for 472/706, 328/214 is 8/75542.