Use our free GCF of Fractions Calculator tool to compute the GCF of 53/49, 414/68, 761/916 i.e 1/763028 easily. The following is the detailed procedure to determine the greatest common factor of fractions 53/49, 414/68, 761/916.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 53/49,414/68,761/916
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 53/49,414/68,761/916, numerators are 53,414,761
Denominators are 49,68,916
The GCF of 53,414,761 is 1 .
LCM of 49,68,916 is 763028.
The greatest common factor of 53/49,414/68,761/916 = [GCF of 53,414,761]/[LCM of 49,68,916]= 1/763028
Therefore, the GCF of 53/49,414/68,761/916 is 1/763028.
To find the highest common factor of 53,414,761, we have to find the factors of both numbers and list the highest common factor.
The factors of 53 are 1, 53
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 761 are 1, 761
The HCF of 53,414,761 is 1.
Lets's calculate GCF of 53,414,761
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 53
:1,53
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 761
:1,761
Greatest Common Factor
We found the factors 53,414,761 . The biggest common factor number is the GCF number.
So the greatest common factor 53,414,761 is 1.
Lets's calculate LCM of 49,68,916
2 | 49, 68, 916 |
2 | 49, 34, 458 |
49, 17, 229 |
∴ So the LCM of the given numbers is 2 x 2 x 49 x 17 x 229 = 763028
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/763028
Therefore, the GCF of Fractions 53/49,414/68,761/916 is 1/763028
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 49,68,916 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,68,916) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(49,68,916) x common factors =1 x 4 = 4
LCM(49,68,916) = ( 49 × 68 × 916 ) / 4
LCM(49,68,916) = 3052112 / 4
LCM(49,68,916) = 763028
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 53,414,761?
The HCF of 53,414,761 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 53/49, 414/68, 761/916?
Answer: GCF of Numerators as per given numbers 53/49, 414/68, 761/916 is
GCF of Numerators i.e. for 53,414,761 is 1
LCM of denominators i.e. for 49,68,916 is 763028.
Thus, GCF of Fractions is 1/763028.Finally, GCF of Fractions for 53/49, 414/68, 761/916 is 1/763028.