Use our free GCF of Fractions Calculator tool to compute the GCF of 107/164, 312/941 i.e 1/154324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 107/164, 312/941.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 107/164,312/941
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 107/164,312/941, numerators are 107,312
Denominators are 164,941
The GCF of 107,312 is 1 .
LCM of 164,941 is 154324.
The greatest common factor of 107/164,312/941 = [GCF of 107,312]/[LCM of 164,941]= 1/154324
Therefore, the GCF of 107/164,312/941 is 1/154324.
To find the highest common factor of 107,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 107 are 1, 107
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 107,312 is 1.
Lets's calculate GCF of 107,312
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 107
:1,107
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 107,312 . The biggest common factor number is the GCF number.
So the greatest common factor 107,312 is 1.
Lets's calculate LCM of 164,941
Given numbers has no common factors except 1. So, there LCM is their product i.e 154324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/154324
Therefore, the GCF of Fractions 107/164,312/941 is 1/154324
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 164,941 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,941) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(164,941) x common factors =1 x 1 = 1
LCM(164,941) = ( 164 × 941 ) / 1
LCM(164,941) = 154324 / 1
LCM(164,941) = 154324
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 107,312?
The HCF of 107,312 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 107/164, 312/941?
Answer: GCF of Numerators as per given numbers 107/164, 312/941 is
GCF of Numerators i.e. for 107,312 is 1
LCM of denominators i.e. for 164,941 is 154324.
Thus, GCF of Fractions is 1/154324.Finally, GCF of Fractions for 107/164, 312/941 is 1/154324.