Use our free GCF of Fractions Calculator tool to compute the GCF of 876/414, 723/905 i.e 3/374670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 876/414, 723/905.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 876/414,723/905
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 876/414,723/905, numerators are 876,723
Denominators are 414,905
The GCF of 876,723 is 3 .
LCM of 414,905 is 374670.
The greatest common factor of 876/414,723/905 = [GCF of 876,723]/[LCM of 414,905]= 3/374670
Therefore, the GCF of 876/414,723/905 is 3/374670.
To find the highest common factor of 876,723, we have to find the factors of both numbers and list the highest common factor.
The factors of 876 are 1, 2, 3, 4, 6, 12, 73, 146, 219, 292, 438, 876
The factors of 723 are 1, 3, 241, 723
The HCF of 876,723 is 3.
Lets's calculate GCF of 876,723
3 | 876, 723 |
292, 241 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 876
:1,2,3,4,6,12,73,146,219,292,438,876
Now, list down the factors of 723
:1,3,241,723
Greatest Common Factor
We found the factors 876,723 . The biggest common factor number is the GCF number.
So the greatest common factor 876,723 is 3.
Lets's calculate LCM of 414,905
Given numbers has no common factors except 1. So, there LCM is their product i.e 374670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/374670
Therefore, the GCF of Fractions 876/414,723/905 is 3/374670
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 414,905 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,905) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(414,905) x common factors =1 x 1 = 1
LCM(414,905) = ( 414 × 905 ) / 1
LCM(414,905) = 374670 / 1
LCM(414,905) = 374670
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 876,723?
The HCF of 876,723 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 876/414, 723/905?
Answer: GCF of Numerators as per given numbers 876/414, 723/905 is
GCF of Numerators i.e. for 876,723 is 3
LCM of denominators i.e. for 414,905 is 374670.
Thus, GCF of Fractions is 3/374670.Finally, GCF of Fractions for 876/414, 723/905 is 3/374670.