GCF of 1971/345, 1740/7889
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1971/345, 1740/7889 i.e 3/118335 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1971/345, 1740/7889.
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 1971/345,1740/7889?
Given fractions are 1971/345,1740/7889
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 1971/345,1740/7889, numerators are 1971,1740
Denominators are 345,7889
The GCF of 1971,1740 is 3 .
LCM of 345,7889 is 118335.
The greatest common factor of 1971/345,1740/7889 = [GCF of 1971,1740]/[LCM of 345,7889]= 3/118335
Therefore, the GCF of 1971/345,1740/7889 is 3/118335.
To find the highest common factor of 1971,1740, we have to find the factors of both numbers and list the highest common factor.
The factors of 1971 are 1, 3, 9, 27, 73, 219, 657, 1971
The factors of 1740 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870, 1740
The HCF of 1971,1740 is 3.
Lets's calculate GCF of 1971,1740
| 3 | 1971, 1740 |
| 657, 580 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1971,1740 By Matching Biggest Common Factor Method
Now, list down the factors of 1971
:1,3,9,27,73,219,657,1971
Now, list down the factors of 1740
:1,2,3,4,5,6,10,12,15,20,29,30,58,60,87,116,145,174,290,348,435,580,870,1740
Greatest Common Factor
We found the factors 1971,1740 . The biggest common factor number is the GCF number.
So the greatest common factor 1971,1740 is 3.
Lets's calculate LCM of 345,7889
| 23 | 345, 7889 |
| 15, 343 |
∴ So the LCM of the given numbers is 23 x 15 x 343 = 118335
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/118335
Therefore, the GCF of Fractions 1971/345,1740/7889 is 3/118335
Least Common Multiple of 345,7889 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 345,7889 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(345,7889) = 23
common factors(in case of two or more numbers have common factors) = 1
GCF(345,7889) x common factors =23 x 1 = 23
LCM(345,7889) = ( 345 × 7889 ) / 23
LCM(345,7889) = 2721705 / 23
LCM(345,7889) = 118335
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FAQs on GCF of Fractions of 1971/345, 1740/7889
1. What is the HCF of 1971,1740?
The HCF of 1971,1740 is 3
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 1971/345, 1740/7889?
Answer: GCF of Numerators as per given numbers 1971/345, 1740/7889 is
GCF of Numerators i.e. for 1971,1740 is 3
LCM of denominators i.e. for 345,7889 is 118335.
Thus, GCF of Fractions is 3/118335.Finally, GCF of Fractions for 1971/345, 1740/7889 is 3/118335.