Use our free GCF of Fractions Calculator tool to compute the GCF of 3782/763, 7657/461 i.e 31/351743 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3782/763, 7657/461.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 3782/763,7657/461
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 3782/763,7657/461, numerators are 3782,7657
Denominators are 763,461
The GCF of 3782,7657 is 31 .
LCM of 763,461 is 351743.
The greatest common factor of 3782/763,7657/461 = [GCF of 3782,7657]/[LCM of 763,461]= 31/351743
Therefore, the GCF of 3782/763,7657/461 is 31/351743.
To find the highest common factor of 3782,7657, we have to find the factors of both numbers and list the highest common factor.
The factors of 3782 are 1, 2, 31, 61, 62, 122, 1891, 3782
The factors of 7657 are 1, 13, 19, 31, 247, 403, 589, 7657
The HCF of 3782,7657 is 31.
Lets's calculate GCF of 3782,7657
31 | 3782, 7657 |
122, 247 |
∴ So the GCF of the given numbers is 31 = 31
Now, list down the factors of 3782
:1,2,31,61,62,122,1891,3782
Now, list down the factors of 7657
:1,13,19,31,247,403,589,7657
Greatest Common Factor
We found the factors 3782,7657 . The biggest common factor number is the GCF number.
So the greatest common factor 3782,7657 is 31.
Lets's calculate LCM of 763,461
Given numbers has no common factors except 1. So, there LCM is their product i.e 351743
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/351743
Therefore, the GCF of Fractions 3782/763,7657/461 is 31/351743
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 763,461 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(763,461) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(763,461) x common factors =1 x 1 = 1
LCM(763,461) = ( 763 × 461 ) / 1
LCM(763,461) = 351743 / 1
LCM(763,461) = 351743
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 3782,7657?
The HCF of 3782,7657 is 31
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 3782/763, 7657/461?
Answer: GCF of Numerators as per given numbers 3782/763, 7657/461 is
GCF of Numerators i.e. for 3782,7657 is 31
LCM of denominators i.e. for 763,461 is 351743.
Thus, GCF of Fractions is 31/351743.Finally, GCF of Fractions for 3782/763, 7657/461 is 31/351743.