GCF of 8/71, 76/55, 42/166, 428/296
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/71, 76/55, 42/166, 428/296 i.e 2/95938040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/71, 76/55, 42/166, 428/296.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 8/71,76/55,42/166,428/296?
Given fractions are 8/71,76/55,42/166,428/296
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 8/71,76/55,42/166,428/296, numerators are 8,76,42,428
Denominators are 71,55,166,296
The GCF of 8,76,42,428 is 2 .
LCM of 71,55,166,296 is 95938040.
The greatest common factor of 8/71,76/55,42/166,428/296 = [GCF of 8,76,42,428]/[LCM of 71,55,166,296]= 2/95938040
Therefore, the GCF of 8/71,76/55,42/166,428/296 is 2/95938040.
To find the highest common factor of 8,76,42,428, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 428 are 1, 2, 4, 107, 214, 428
The HCF of 8,76,42,428 is 2.
Lets's calculate GCF of 8,76,42,428
| 2 | 8, 76, 42, 428 |
| 4, 38, 21, 214 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8,76,42,428 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 428
:1,2,4,107,214,428
Greatest Common Factor
We found the factors 8,76,42,428 . The biggest common factor number is the GCF number.
So the greatest common factor 8,76,42,428 is 2.
Lets's calculate LCM of 71,55,166,296
| 2 | 71, 55, 166, 296 |
| 71, 55, 83, 148 |
∴ So the LCM of the given numbers is 2 x 71 x 55 x 83 x 148 = 95938040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/95938040
Therefore, the GCF of Fractions 8/71,76/55,42/166,428/296 is 2/95938040
Least Common Multiple of 71,55,166,296 with GCF Formula
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 71,55,166,296 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,55,166,296) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(71,55,166,296) x common factors =1 x 2 = 2
LCM(71,55,166,296) = ( 71 × 55 × 166 × 296 ) / 2
LCM(71,55,166,296) = 191876080 / 2
LCM(71,55,166,296) = 95938040
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 8/71, 76/55, 42/166, 428/296
1. What is the HCF of 8,76,42,428?
The HCF of 8,76,42,428 is 2
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 8/71, 76/55, 42/166, 428/296?
Answer: GCF of Numerators as per given numbers 8/71, 76/55, 42/166, 428/296 is
GCF of Numerators i.e. for 8,76,42,428 is 2
LCM of denominators i.e. for 71,55,166,296 is 95938040.
Thus, GCF of Fractions is 2/95938040.Finally, GCF of Fractions for 8/71, 76/55, 42/166, 428/296 is 2/95938040.