GCF of 138/221, 109/312, 591/325
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 138/221, 109/312, 591/325 i.e 1/132600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 138/221, 109/312, 591/325.
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 138/221,109/312,591/325?
Given fractions are 138/221,109/312,591/325
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 138/221,109/312,591/325, numerators are 138,109,591
Denominators are 221,312,325
The GCF of 138,109,591 is 1 .
LCM of 221,312,325 is 132600.
The greatest common factor of 138/221,109/312,591/325 = [GCF of 138,109,591]/[LCM of 221,312,325]= 1/132600
Therefore, the GCF of 138/221,109/312,591/325 is 1/132600.
To find the highest common factor of 138,109,591, we have to find the factors of both numbers and list the highest common factor.
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The factors of 109 are 1, 109
The factors of 591 are 1, 3, 197, 591
The HCF of 138,109,591 is 1.
Lets's calculate GCF of 138,109,591
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 138,109,591 By Matching Biggest Common Factor Method
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Now, list down the factors of 109
:1,109
Now, list down the factors of 591
:1,3,197,591
Greatest Common Factor
We found the factors 138,109,591 . The biggest common factor number is the GCF number.
So the greatest common factor 138,109,591 is 1.
Lets's calculate LCM of 221,312,325
| 13 | 221, 312, 325 |
| 17, 24, 25 |
∴ So the LCM of the given numbers is 13 x 17 x 24 x 25 = 132600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/132600
Therefore, the GCF of Fractions 138/221,109/312,591/325 is 1/132600
Least Common Multiple of 221,312,325 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 221,312,325 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(221,312,325) = 13
common factors(in case of two or more numbers have common factors) = 13
GCF(221,312,325) x common factors =13 x 13 = 169
LCM(221,312,325) = ( 221 × 312 × 325 ) / 169
LCM(221,312,325) = 22409400 / 169
LCM(221,312,325) = 132600
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FAQs on GCF of Fractions of 138/221, 109/312, 591/325
1. What is the HCF of 138,109,591?
The HCF of 138,109,591 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 138/221, 109/312, 591/325?
Answer: GCF of Numerators as per given numbers 138/221, 109/312, 591/325 is
GCF of Numerators i.e. for 138,109,591 is 1
LCM of denominators i.e. for 221,312,325 is 132600.
Thus, GCF of Fractions is 1/132600.Finally, GCF of Fractions for 138/221, 109/312, 591/325 is 1/132600.