GCF of 342/185, 189/319
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 342/185, 189/319 i.e 9/59015 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/185, 189/319.
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 342/185,189/319?
Given fractions are 342/185,189/319
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 342/185,189/319, numerators are 342,189
Denominators are 185,319
The GCF of 342,189 is 9 .
LCM of 185,319 is 59015.
The greatest common factor of 342/185,189/319 = [GCF of 342,189]/[LCM of 185,319]= 9/59015
Therefore, the GCF of 342/185,189/319 is 9/59015.
To find the highest common factor of 342,189, we have to find the factors of both numbers and list the highest common factor.
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The HCF of 342,189 is 9.
Lets's calculate GCF of 342,189
| 3 | 342, 189 |
| 3 | 114, 63 |
| 38, 21 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 342,189 By Matching Biggest Common Factor Method
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Greatest Common Factor
We found the factors 342,189 . The biggest common factor number is the GCF number.
So the greatest common factor 342,189 is 9.
Lets's calculate LCM of 185,319
Given numbers has no common factors except 1. So, there LCM is their product i.e 59015
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/59015
Therefore, the GCF of Fractions 342/185,189/319 is 9/59015
Least Common Multiple of 185,319 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 185,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(185,319) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(185,319) x common factors =1 x 1 = 1
LCM(185,319) = ( 185 × 319 ) / 1
LCM(185,319) = 59015 / 1
LCM(185,319) = 59015
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FAQs on GCF of Fractions of 342/185, 189/319
1. What is the HCF of 342,189?
The HCF of 342,189 is 9
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 342/185, 189/319?
Answer: GCF of Numerators as per given numbers 342/185, 189/319 is
GCF of Numerators i.e. for 342,189 is 9
LCM of denominators i.e. for 185,319 is 59015.
Thus, GCF of Fractions is 9/59015.Finally, GCF of Fractions for 342/185, 189/319 is 9/59015.