GCF of 589/68, 698/1766
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 589/68, 698/1766 i.e 1/60044 easily. The following is the detailed procedure to determine the greatest common factor of fractions 589/68, 698/1766.
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 589/68,698/1766?
Given fractions are 589/68,698/1766
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 589/68,698/1766, numerators are 589,698
Denominators are 68,1766
The GCF of 589,698 is 1 .
LCM of 68,1766 is 60044.
The greatest common factor of 589/68,698/1766 = [GCF of 589,698]/[LCM of 68,1766]= 1/60044
Therefore, the GCF of 589/68,698/1766 is 1/60044.
To find the highest common factor of 589,698, 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 698 are 1, 2, 349, 698
The HCF of 589,698 is 1.
Lets's calculate GCF of 589,698
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 589,698 By Matching Biggest Common Factor Method
Now, list down the factors of 589
:1,19,31,589
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 589,698 . The biggest common factor number is the GCF number.
So the greatest common factor 589,698 is 1.
Lets's calculate LCM of 68,1766
| 2 | 68, 1766 |
| 34, 883 |
∴ So the LCM of the given numbers is 2 x 34 x 883 = 60044
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/60044
Therefore, the GCF of Fractions 589/68,698/1766 is 1/60044
Least Common Multiple of 68,1766 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 68,1766 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,1766) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(68,1766) x common factors =2 x 1 = 2
LCM(68,1766) = ( 68 × 1766 ) / 2
LCM(68,1766) = 120088 / 2
LCM(68,1766) = 60044
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FAQs on GCF of Fractions of 589/68, 698/1766
1. What is the HCF of 589,698?
The HCF of 589,698 is 1
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 589/68, 698/1766?
Answer: GCF of Numerators as per given numbers 589/68, 698/1766 is
GCF of Numerators i.e. for 589,698 is 1
LCM of denominators i.e. for 68,1766 is 60044.
Thus, GCF of Fractions is 1/60044.Finally, GCF of Fractions for 589/68, 698/1766 is 1/60044.