GCF of 488/322, 5978/577
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 488/322, 5978/577 i.e 122/185794 easily. The following is the detailed procedure to determine the greatest common factor of fractions 488/322, 5978/577.
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 488/322,5978/577?
Given fractions are 488/322,5978/577
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 488/322,5978/577, numerators are 488,5978
Denominators are 322,577
The GCF of 488,5978 is 122 .
LCM of 322,577 is 185794.
The greatest common factor of 488/322,5978/577 = [GCF of 488,5978]/[LCM of 322,577]= 122/185794
Therefore, the GCF of 488/322,5978/577 is 122/185794.
To find the highest common factor of 488,5978, we have to find the factors of both numbers and list the highest common factor.
The factors of 488 are 1, 2, 4, 8, 61, 122, 244, 488
The factors of 5978 are 1, 2, 7, 14, 49, 61, 98, 122, 427, 854, 2989, 5978
The HCF of 488,5978 is 122.
Lets's calculate GCF of 488,5978
| 2 | 488, 5978 |
| 61 | 244, 2989 |
| 4, 49 |
∴ So the GCF of the given numbers is 2 x 61 = 122
Greatest Common Factor of 488,5978 By Matching Biggest Common Factor Method
Now, list down the factors of 488
:1,2,4,8,61,122,244,488
Now, list down the factors of 5978
:1,2,7,14,49,61,98,122,427,854,2989,5978
Greatest Common Factor
We found the factors 488,5978 . The biggest common factor number is the GCF number.
So the greatest common factor 488,5978 is 122.
Lets's calculate LCM of 322,577
Given numbers has no common factors except 1. So, there LCM is their product i.e 185794
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 122/185794
Therefore, the GCF of Fractions 488/322,5978/577 is 122/185794
Least Common Multiple of 322,577 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 322,577 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(322,577) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(322,577) x common factors =1 x 1 = 1
LCM(322,577) = ( 322 × 577 ) / 1
LCM(322,577) = 185794 / 1
LCM(322,577) = 185794
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FAQs on GCF of Fractions of 488/322, 5978/577
1. What is the HCF of 488,5978?
The HCF of 488,5978 is 122
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 488/322, 5978/577?
Answer: GCF of Numerators as per given numbers 488/322, 5978/577 is
GCF of Numerators i.e. for 488,5978 is 122
LCM of denominators i.e. for 322,577 is 185794.
Thus, GCF of Fractions is 122/185794.Finally, GCF of Fractions for 488/322, 5978/577 is 122/185794.