GCF of 199/77, 589/154
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 199/77, 589/154 i.e 1/154 easily. The following is the detailed procedure to determine the greatest common factor of fractions 199/77, 589/154.
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 199/77,589/154?
Given fractions are 199/77,589/154
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 199/77,589/154, numerators are 199,589
Denominators are 77,154
The GCF of 199,589 is 1 .
LCM of 77,154 is 154.
The greatest common factor of 199/77,589/154 = [GCF of 199,589]/[LCM of 77,154]= 1/154
Therefore, the GCF of 199/77,589/154 is 1/154.
To find the highest common factor of 199,589, we have to find the factors of both numbers and list the highest common factor.
The factors of 199 are 1, 199
The factors of 589 are 1, 19, 31, 589
The HCF of 199,589 is 1.
Lets's calculate GCF of 199,589
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 199,589 By Matching Biggest Common Factor Method
Now, list down the factors of 199
:1,199
Now, list down the factors of 589
:1,19,31,589
Greatest Common Factor
We found the factors 199,589 . The biggest common factor number is the GCF number.
So the greatest common factor 199,589 is 1.
Lets's calculate LCM of 77,154
| 7 | 77, 154 |
| 11 | 11, 22 |
| 1, 2 |
∴ So the LCM of the given numbers is 7 x 11 x 1 x 2 = 154
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/154
Therefore, the GCF of Fractions 199/77,589/154 is 1/154
Least Common Multiple of 77,154 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 77,154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,154) = 77
common factors(in case of two or more numbers have common factors) = 1
GCF(77,154) x common factors =77 x 1 = 77
LCM(77,154) = ( 77 × 154 ) / 77
LCM(77,154) = 11858 / 77
LCM(77,154) = 154
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FAQs on GCF of Fractions of 199/77, 589/154
1. What is the HCF of 199,589?
The HCF of 199,589 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 199/77, 589/154?
Answer: GCF of Numerators as per given numbers 199/77, 589/154 is
GCF of Numerators i.e. for 199,589 is 1
LCM of denominators i.e. for 77,154 is 154.
Thus, GCF of Fractions is 1/154.Finally, GCF of Fractions for 199/77, 589/154 is 1/154.