GCF of 187/15, 306/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 187/15, 306/419 i.e 17/6285 easily. The following is the detailed procedure to determine the greatest common factor of fractions 187/15, 306/419.
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 187/15,306/419?
Given fractions are 187/15,306/419
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 187/15,306/419, numerators are 187,306
Denominators are 15,419
The GCF of 187,306 is 17 .
LCM of 15,419 is 6285.
The greatest common factor of 187/15,306/419 = [GCF of 187,306]/[LCM of 15,419]= 17/6285
Therefore, the GCF of 187/15,306/419 is 17/6285.
To find the highest common factor of 187,306, we have to find the factors of both numbers and list the highest common factor.
The factors of 187 are 1, 11, 17, 187
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The HCF of 187,306 is 17.
Lets's calculate GCF of 187,306
| 17 | 187, 306 |
| 11, 18 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 187,306 By Matching Biggest Common Factor Method
Now, list down the factors of 187
:1,11,17,187
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Greatest Common Factor
We found the factors 187,306 . The biggest common factor number is the GCF number.
So the greatest common factor 187,306 is 17.
Lets's calculate LCM of 15,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 6285
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/6285
Therefore, the GCF of Fractions 187/15,306/419 is 17/6285
Least Common Multiple of 15,419 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 15,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(15,419) x common factors =1 x 1 = 1
LCM(15,419) = ( 15 × 419 ) / 1
LCM(15,419) = 6285 / 1
LCM(15,419) = 6285
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FAQs on GCF of Fractions of 187/15, 306/419
1. What is the HCF of 187,306?
The HCF of 187,306 is 17
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 187/15, 306/419?
Answer: GCF of Numerators as per given numbers 187/15, 306/419 is
GCF of Numerators i.e. for 187,306 is 17
LCM of denominators i.e. for 15,419 is 6285.
Thus, GCF of Fractions is 17/6285.Finally, GCF of Fractions for 187/15, 306/419 is 17/6285.