Use our free GCF of Fractions Calculator tool to compute the GCF of 212/788, 316/706 i.e 4/278164 easily. The following is the detailed procedure to determine the greatest common factor of fractions 212/788, 316/706.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 212/788,316/706
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 212/788,316/706, numerators are 212,316
Denominators are 788,706
The GCF of 212,316 is 4 .
LCM of 788,706 is 278164.
The greatest common factor of 212/788,316/706 = [GCF of 212,316]/[LCM of 788,706]= 4/278164
Therefore, the GCF of 212/788,316/706 is 4/278164.
To find the highest common factor of 212,316, we have to find the factors of both numbers and list the highest common factor.
The factors of 212 are 1, 2, 4, 53, 106, 212
The factors of 316 are 1, 2, 4, 79, 158, 316
The HCF of 212,316 is 4.
Lets's calculate GCF of 212,316
2 | 212, 316 |
2 | 106, 158 |
53, 79 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 212
:1,2,4,53,106,212
Now, list down the factors of 316
:1,2,4,79,158,316
Greatest Common Factor
We found the factors 212,316 . The biggest common factor number is the GCF number.
So the greatest common factor 212,316 is 4.
Lets's calculate LCM of 788,706
2 | 788, 706 |
394, 353 |
∴ So the LCM of the given numbers is 2 x 394 x 353 = 278164
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/278164
Therefore, the GCF of Fractions 212/788,316/706 is 4/278164
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 788,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(788,706) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(788,706) x common factors =2 x 1 = 2
LCM(788,706) = ( 788 × 706 ) / 2
LCM(788,706) = 556328 / 2
LCM(788,706) = 278164
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 212,316?
The HCF of 212,316 is 4
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 212/788, 316/706?
Answer: GCF of Numerators as per given numbers 212/788, 316/706 is
GCF of Numerators i.e. for 212,316 is 4
LCM of denominators i.e. for 788,706 is 278164.
Thus, GCF of Fractions is 4/278164.Finally, GCF of Fractions for 212/788, 316/706 is 4/278164.