GCF of 589/658, 992/321
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 589/658, 992/321 i.e 31/211218 easily. The following is the detailed procedure to determine the greatest common factor of fractions 589/658, 992/321.
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 589/658,992/321?
Given fractions are 589/658,992/321
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 589/658,992/321, numerators are 589,992
Denominators are 658,321
The GCF of 589,992 is 31 .
LCM of 658,321 is 211218.
The greatest common factor of 589/658,992/321 = [GCF of 589,992]/[LCM of 658,321]= 31/211218
Therefore, the GCF of 589/658,992/321 is 31/211218.
To find the highest common factor of 589,992, we have to find the factors of both numbers and list the highest common factor.
The factors of 589 are 1, 19, 31, 589
The factors of 992 are 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992
The HCF of 589,992 is 31.
Lets's calculate GCF of 589,992
| 31 | 589, 992 |
| 19, 32 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 589,992 By Matching Biggest Common Factor Method
Now, list down the factors of 589
:1,19,31,589
Now, list down the factors of 992
:1,2,4,8,16,31,32,62,124,248,496,992
Greatest Common Factor
We found the factors 589,992 . The biggest common factor number is the GCF number.
So the greatest common factor 589,992 is 31.
Lets's calculate LCM of 658,321
Given numbers has no common factors except 1. So, there LCM is their product i.e 211218
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/211218
Therefore, the GCF of Fractions 589/658,992/321 is 31/211218
Least Common Multiple of 658,321 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 658,321 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(658,321) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(658,321) x common factors =1 x 1 = 1
LCM(658,321) = ( 658 × 321 ) / 1
LCM(658,321) = 211218 / 1
LCM(658,321) = 211218
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FAQs on GCF of Fractions of 589/658, 992/321
1. What is the HCF of 589,992?
The HCF of 589,992 is 31
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 589/658, 992/321?
Answer: GCF of Numerators as per given numbers 589/658, 992/321 is
GCF of Numerators i.e. for 589,992 is 31
LCM of denominators i.e. for 658,321 is 211218.
Thus, GCF of Fractions is 31/211218.Finally, GCF of Fractions for 589/658, 992/321 is 31/211218.