GCF of 978/39, 590/139
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 978/39, 590/139 i.e 2/5421 easily. The following is the detailed procedure to determine the greatest common factor of fractions 978/39, 590/139.
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 978/39,590/139?
Given fractions are 978/39,590/139
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 978/39,590/139, numerators are 978,590
Denominators are 39,139
The GCF of 978,590 is 2 .
LCM of 39,139 is 5421.
The greatest common factor of 978/39,590/139 = [GCF of 978,590]/[LCM of 39,139]= 2/5421
Therefore, the GCF of 978/39,590/139 is 2/5421.
To find the highest common factor of 978,590, we have to find the factors of both numbers and list the highest common factor.
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590
The HCF of 978,590 is 2.
Lets's calculate GCF of 978,590
| 2 | 978, 590 |
| 489, 295 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 978,590 By Matching Biggest Common Factor Method
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Now, list down the factors of 590
:1,2,5,10,59,118,295,590
Greatest Common Factor
We found the factors 978,590 . The biggest common factor number is the GCF number.
So the greatest common factor 978,590 is 2.
Lets's calculate LCM of 39,139
Given numbers has no common factors except 1. So, there LCM is their product i.e 5421
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5421
Therefore, the GCF of Fractions 978/39,590/139 is 2/5421
Least Common Multiple of 39,139 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 39,139 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,139) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(39,139) x common factors =1 x 1 = 1
LCM(39,139) = ( 39 × 139 ) / 1
LCM(39,139) = 5421 / 1
LCM(39,139) = 5421
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FAQs on GCF of Fractions of 978/39, 590/139
1. What is the HCF of 978,590?
The HCF of 978,590 is 2
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 978/39, 590/139?
Answer: GCF of Numerators as per given numbers 978/39, 590/139 is
GCF of Numerators i.e. for 978,590 is 2
LCM of denominators i.e. for 39,139 is 5421.
Thus, GCF of Fractions is 2/5421.Finally, GCF of Fractions for 978/39, 590/139 is 2/5421.