GCF of 14/75, 80/20, 538/271
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/75, 80/20, 538/271 i.e 2/81300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/75, 80/20, 538/271.
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 14/75,80/20,538/271?
Given fractions are 14/75,80/20,538/271
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 14/75,80/20,538/271, numerators are 14,80,538
Denominators are 75,20,271
The GCF of 14,80,538 is 2 .
LCM of 75,20,271 is 81300.
The greatest common factor of 14/75,80/20,538/271 = [GCF of 14,80,538]/[LCM of 75,20,271]= 2/81300
Therefore, the GCF of 14/75,80/20,538/271 is 2/81300.
To find the highest common factor of 14,80,538, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 538 are 1, 2, 269, 538
The HCF of 14,80,538 is 2.
Lets's calculate GCF of 14,80,538
| 2 | 14, 80, 538 |
| 7, 40, 269 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 14,80,538 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 538
:1,2,269,538
Greatest Common Factor
We found the factors 14,80,538 . The biggest common factor number is the GCF number.
So the greatest common factor 14,80,538 is 2.
Lets's calculate LCM of 75,20,271
| 5 | 75, 20, 271 |
| 15, 4, 271 |
∴ So the LCM of the given numbers is 5 x 15 x 4 x 271 = 81300
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/81300
Therefore, the GCF of Fractions 14/75,80/20,538/271 is 2/81300
Least Common Multiple of 75,20,271 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 75,20,271 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,20,271) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(75,20,271) x common factors =1 x 5 = 5
LCM(75,20,271) = ( 75 × 20 × 271 ) / 5
LCM(75,20,271) = 406500 / 5
LCM(75,20,271) = 81300
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FAQs on GCF of Fractions of 14/75, 80/20, 538/271
1. What is the HCF of 14,80,538?
The HCF of 14,80,538 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 14/75, 80/20, 538/271?
Answer: GCF of Numerators as per given numbers 14/75, 80/20, 538/271 is
GCF of Numerators i.e. for 14,80,538 is 2
LCM of denominators i.e. for 75,20,271 is 81300.
Thus, GCF of Fractions is 2/81300.Finally, GCF of Fractions for 14/75, 80/20, 538/271 is 2/81300.