Use our free GCF of Fractions Calculator tool to compute the GCF of 53/76, 985/42, 114/254 i.e 1/202692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 53/76, 985/42, 114/254.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 53/76,985/42,114/254
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 53/76,985/42,114/254, numerators are 53,985,114
Denominators are 76,42,254
The GCF of 53,985,114 is 1 .
LCM of 76,42,254 is 202692.
The greatest common factor of 53/76,985/42,114/254 = [GCF of 53,985,114]/[LCM of 76,42,254]= 1/202692
Therefore, the GCF of 53/76,985/42,114/254 is 1/202692.
To find the highest common factor of 53,985,114, 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 985 are 1, 5, 197, 985
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The HCF of 53,985,114 is 1.
Lets's calculate GCF of 53,985,114
∴ 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 985
:1,5,197,985
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Greatest Common Factor
We found the factors 53,985,114 . The biggest common factor number is the GCF number.
So the greatest common factor 53,985,114 is 1.
Lets's calculate LCM of 76,42,254
2 | 76, 42, 254 |
38, 21, 127 |
∴ So the LCM of the given numbers is 2 x 38 x 21 x 127 = 202692
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/202692
Therefore, the GCF of Fractions 53/76,985/42,114/254 is 1/202692
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 76,42,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,42,254) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(76,42,254) x common factors =2 x 2 = 4
LCM(76,42,254) = ( 76 × 42 × 254 ) / 4
LCM(76,42,254) = 810768 / 4
LCM(76,42,254) = 202692
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 53,985,114?
The HCF of 53,985,114 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 53/76, 985/42, 114/254?
Answer: GCF of Numerators as per given numbers 53/76, 985/42, 114/254 is
GCF of Numerators i.e. for 53,985,114 is 1
LCM of denominators i.e. for 76,42,254 is 202692.
Thus, GCF of Fractions is 1/202692.Finally, GCF of Fractions for 53/76, 985/42, 114/254 is 1/202692.