GCF of 489/194, 5778/2122
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 489/194, 5778/2122 i.e 3/205834 easily. The following is the detailed procedure to determine the greatest common factor of fractions 489/194, 5778/2122.
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 489/194,5778/2122?
Given fractions are 489/194,5778/2122
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 489/194,5778/2122, numerators are 489,5778
Denominators are 194,2122
The GCF of 489,5778 is 3 .
LCM of 194,2122 is 205834.
The greatest common factor of 489/194,5778/2122 = [GCF of 489,5778]/[LCM of 194,2122]= 3/205834
Therefore, the GCF of 489/194,5778/2122 is 3/205834.
To find the highest common factor of 489,5778, we have to find the factors of both numbers and list the highest common factor.
The factors of 489 are 1, 3, 163, 489
The factors of 5778 are 1, 2, 3, 6, 9, 18, 27, 54, 107, 214, 321, 642, 963, 1926, 2889, 5778
The HCF of 489,5778 is 3.
Lets's calculate GCF of 489,5778
| 3 | 489, 5778 |
| 163, 1926 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 489,5778 By Matching Biggest Common Factor Method
Now, list down the factors of 489
:1,3,163,489
Now, list down the factors of 5778
:1,2,3,6,9,18,27,54,107,214,321,642,963,1926,2889,5778
Greatest Common Factor
We found the factors 489,5778 . The biggest common factor number is the GCF number.
So the greatest common factor 489,5778 is 3.
Lets's calculate LCM of 194,2122
| 2 | 194, 2122 |
| 97, 1061 |
∴ So the LCM of the given numbers is 2 x 97 x 1061 = 205834
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/205834
Therefore, the GCF of Fractions 489/194,5778/2122 is 3/205834
Least Common Multiple of 194,2122 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 194,2122 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(194,2122) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(194,2122) x common factors =2 x 1 = 2
LCM(194,2122) = ( 194 × 2122 ) / 2
LCM(194,2122) = 411668 / 2
LCM(194,2122) = 205834
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FAQs on GCF of Fractions of 489/194, 5778/2122
1. What is the HCF of 489,5778?
The HCF of 489,5778 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 489/194, 5778/2122?
Answer: GCF of Numerators as per given numbers 489/194, 5778/2122 is
GCF of Numerators i.e. for 489,5778 is 3
LCM of denominators i.e. for 194,2122 is 205834.
Thus, GCF of Fractions is 3/205834.Finally, GCF of Fractions for 489/194, 5778/2122 is 3/205834.