GCF of 138/218, 575/398
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 138/218, 575/398 i.e 23/43382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 138/218, 575/398.
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 138/218,575/398?
Given fractions are 138/218,575/398
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 138/218,575/398, numerators are 138,575
Denominators are 218,398
The GCF of 138,575 is 23 .
LCM of 218,398 is 43382.
The greatest common factor of 138/218,575/398 = [GCF of 138,575]/[LCM of 218,398]= 23/43382
Therefore, the GCF of 138/218,575/398 is 23/43382.
To find the highest common factor of 138,575, 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 575 are 1, 5, 23, 25, 115, 575
The HCF of 138,575 is 23.
Lets's calculate GCF of 138,575
| 23 | 138, 575 |
| 6, 25 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 138,575 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 575
:1,5,23,25,115,575
Greatest Common Factor
We found the factors 138,575 . The biggest common factor number is the GCF number.
So the greatest common factor 138,575 is 23.
Lets's calculate LCM of 218,398
| 2 | 218, 398 |
| 109, 199 |
∴ So the LCM of the given numbers is 2 x 109 x 199 = 43382
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/43382
Therefore, the GCF of Fractions 138/218,575/398 is 23/43382
Least Common Multiple of 218,398 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 218,398 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,398) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(218,398) x common factors =2 x 1 = 2
LCM(218,398) = ( 218 × 398 ) / 2
LCM(218,398) = 86764 / 2
LCM(218,398) = 43382
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FAQs on GCF of Fractions of 138/218, 575/398
1. What is the HCF of 138,575?
The HCF of 138,575 is 23
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 138/218, 575/398?
Answer: GCF of Numerators as per given numbers 138/218, 575/398 is
GCF of Numerators i.e. for 138,575 is 23
LCM of denominators i.e. for 218,398 is 43382.
Thus, GCF of Fractions is 23/43382.Finally, GCF of Fractions for 138/218, 575/398 is 23/43382.