GCF of 35/84, 538/66, 341/213
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 35/84, 538/66, 341/213 i.e 1/65604 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/84, 538/66, 341/213.
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 35/84,538/66,341/213?
Given fractions are 35/84,538/66,341/213
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 35/84,538/66,341/213, numerators are 35,538,341
Denominators are 84,66,213
The GCF of 35,538,341 is 1 .
LCM of 84,66,213 is 65604.
The greatest common factor of 35/84,538/66,341/213 = [GCF of 35,538,341]/[LCM of 84,66,213]= 1/65604
Therefore, the GCF of 35/84,538/66,341/213 is 1/65604.
To find the highest common factor of 35,538,341, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 538 are 1, 2, 269, 538
The factors of 341 are 1, 11, 31, 341
The HCF of 35,538,341 is 1.
Lets's calculate GCF of 35,538,341
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 35,538,341 By Matching Biggest Common Factor Method
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 538
:1,2,269,538
Now, list down the factors of 341
:1,11,31,341
Greatest Common Factor
We found the factors 35,538,341 . The biggest common factor number is the GCF number.
So the greatest common factor 35,538,341 is 1.
Lets's calculate LCM of 84,66,213
| 2 | 84, 66, 213 |
| 3 | 42, 33, 213 |
| 14, 11, 71 |
∴ So the LCM of the given numbers is 2 x 3 x 14 x 11 x 71 = 65604
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/65604
Therefore, the GCF of Fractions 35/84,538/66,341/213 is 1/65604
Least Common Multiple of 84,66,213 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 84,66,213 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,66,213) = 3
common factors(in case of two or more numbers have common factors) = 6
GCF(84,66,213) x common factors =3 x 6 = 18
LCM(84,66,213) = ( 84 × 66 × 213 ) / 18
LCM(84,66,213) = 1180872 / 18
LCM(84,66,213) = 65604
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 35/84, 538/66, 341/213
1. What is the HCF of 35,538,341?
The HCF of 35,538,341 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 35/84, 538/66, 341/213?
Answer: GCF of Numerators as per given numbers 35/84, 538/66, 341/213 is
GCF of Numerators i.e. for 35,538,341 is 1
LCM of denominators i.e. for 84,66,213 is 65604.
Thus, GCF of Fractions is 1/65604.Finally, GCF of Fractions for 35/84, 538/66, 341/213 is 1/65604.