Use our free GCF of Fractions Calculator tool to compute the GCF of 597/413, 312/914 i.e 3/377482 easily. The following is the detailed procedure to determine the greatest common factor of fractions 597/413, 312/914.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 597/413,312/914
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 597/413,312/914, numerators are 597,312
Denominators are 413,914
The GCF of 597,312 is 3 .
LCM of 413,914 is 377482.
The greatest common factor of 597/413,312/914 = [GCF of 597,312]/[LCM of 413,914]= 3/377482
Therefore, the GCF of 597/413,312/914 is 3/377482.
To find the highest common factor of 597,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 597 are 1, 3, 199, 597
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 597,312 is 3.
Lets's calculate GCF of 597,312
3 | 597, 312 |
199, 104 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 597
:1,3,199,597
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 597,312 . The biggest common factor number is the GCF number.
So the greatest common factor 597,312 is 3.
Lets's calculate LCM of 413,914
Given numbers has no common factors except 1. So, there LCM is their product i.e 377482
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/377482
Therefore, the GCF of Fractions 597/413,312/914 is 3/377482
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 413,914 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,914) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(413,914) x common factors =1 x 1 = 1
LCM(413,914) = ( 413 × 914 ) / 1
LCM(413,914) = 377482 / 1
LCM(413,914) = 377482
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 597,312?
The HCF of 597,312 is 3
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 597/413, 312/914?
Answer: GCF of Numerators as per given numbers 597/413, 312/914 is
GCF of Numerators i.e. for 597,312 is 3
LCM of denominators i.e. for 413,914 is 377482.
Thus, GCF of Fractions is 3/377482.Finally, GCF of Fractions for 597/413, 312/914 is 3/377482.