GCF of 596/31, 230/1991
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 596/31, 230/1991 i.e 2/61721 easily. The following is the detailed procedure to determine the greatest common factor of fractions 596/31, 230/1991.
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 596/31,230/1991?
Given fractions are 596/31,230/1991
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 596/31,230/1991, numerators are 596,230
Denominators are 31,1991
The GCF of 596,230 is 2 .
LCM of 31,1991 is 61721.
The greatest common factor of 596/31,230/1991 = [GCF of 596,230]/[LCM of 31,1991]= 2/61721
Therefore, the GCF of 596/31,230/1991 is 2/61721.
To find the highest common factor of 596,230, we have to find the factors of both numbers and list the highest common factor.
The factors of 596 are 1, 2, 4, 149, 298, 596
The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230
The HCF of 596,230 is 2.
Lets's calculate GCF of 596,230
| 2 | 596, 230 |
| 298, 115 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 596,230 By Matching Biggest Common Factor Method
Now, list down the factors of 596
:1,2,4,149,298,596
Now, list down the factors of 230
:1,2,5,10,23,46,115,230
Greatest Common Factor
We found the factors 596,230 . The biggest common factor number is the GCF number.
So the greatest common factor 596,230 is 2.
Lets's calculate LCM of 31,1991
Given numbers has no common factors except 1. So, there LCM is their product i.e 61721
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/61721
Therefore, the GCF of Fractions 596/31,230/1991 is 2/61721
Least Common Multiple of 31,1991 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 31,1991 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,1991) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,1991) x common factors =1 x 1 = 1
LCM(31,1991) = ( 31 × 1991 ) / 1
LCM(31,1991) = 61721 / 1
LCM(31,1991) = 61721
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FAQs on GCF of Fractions of 596/31, 230/1991
1. What is the HCF of 596,230?
The HCF of 596,230 is 2
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 596/31, 230/1991?
Answer: GCF of Numerators as per given numbers 596/31, 230/1991 is
GCF of Numerators i.e. for 596,230 is 2
LCM of denominators i.e. for 31,1991 is 61721.
Thus, GCF of Fractions is 2/61721.Finally, GCF of Fractions for 596/31, 230/1991 is 2/61721.