GCF of 741/86, 380/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 741/86, 380/209 i.e 19/17974 easily. The following is the detailed procedure to determine the greatest common factor of fractions 741/86, 380/209.
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 741/86,380/209?
Given fractions are 741/86,380/209
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 741/86,380/209, numerators are 741,380
Denominators are 86,209
The GCF of 741,380 is 19 .
LCM of 86,209 is 17974.
The greatest common factor of 741/86,380/209 = [GCF of 741,380]/[LCM of 86,209]= 19/17974
Therefore, the GCF of 741/86,380/209 is 19/17974.
To find the highest common factor of 741,380, we have to find the factors of both numbers and list the highest common factor.
The factors of 741 are 1, 3, 13, 19, 39, 57, 247, 741
The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
The HCF of 741,380 is 19.
Lets's calculate GCF of 741,380
| 19 | 741, 380 |
| 39, 20 |
∴ So the GCF of the given numbers is 19 = 19
Greatest Common Factor of 741,380 By Matching Biggest Common Factor Method
Now, list down the factors of 741
:1,3,13,19,39,57,247,741
Now, list down the factors of 380
:1,2,4,5,10,19,20,38,76,95,190,380
Greatest Common Factor
We found the factors 741,380 . The biggest common factor number is the GCF number.
So the greatest common factor 741,380 is 19.
Lets's calculate LCM of 86,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 17974
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/17974
Therefore, the GCF of Fractions 741/86,380/209 is 19/17974
Least Common Multiple of 86,209 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 86,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(86,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(86,209) x common factors =1 x 1 = 1
LCM(86,209) = ( 86 × 209 ) / 1
LCM(86,209) = 17974 / 1
LCM(86,209) = 17974
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FAQs on GCF of Fractions of 741/86, 380/209
1. What is the HCF of 741,380?
The HCF of 741,380 is 19
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 741/86, 380/209?
Answer: GCF of Numerators as per given numbers 741/86, 380/209 is
GCF of Numerators i.e. for 741,380 is 19
LCM of denominators i.e. for 86,209 is 17974.
Thus, GCF of Fractions is 19/17974.Finally, GCF of Fractions for 741/86, 380/209 is 19/17974.