GCF of 178/420, 978/819
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 178/420, 978/819 i.e 2/16380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 178/420, 978/819.
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 178/420,978/819?
Given fractions are 178/420,978/819
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 178/420,978/819, numerators are 178,978
Denominators are 420,819
The GCF of 178,978 is 2 .
LCM of 420,819 is 16380.
The greatest common factor of 178/420,978/819 = [GCF of 178,978]/[LCM of 420,819]= 2/16380
Therefore, the GCF of 178/420,978/819 is 2/16380.
To find the highest common factor of 178,978, we have to find the factors of both numbers and list the highest common factor.
The factors of 178 are 1, 2, 89, 178
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The HCF of 178,978 is 2.
Lets's calculate GCF of 178,978
| 2 | 178, 978 |
| 89, 489 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 178,978 By Matching Biggest Common Factor Method
Now, list down the factors of 178
:1,2,89,178
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Greatest Common Factor
We found the factors 178,978 . The biggest common factor number is the GCF number.
So the greatest common factor 178,978 is 2.
Lets's calculate LCM of 420,819
| 3 | 420, 819 |
| 7 | 140, 273 |
| 20, 39 |
∴ So the LCM of the given numbers is 3 x 7 x 20 x 39 = 16380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16380
Therefore, the GCF of Fractions 178/420,978/819 is 2/16380
Least Common Multiple of 420,819 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 420,819 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,819) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(420,819) x common factors =21 x 1 = 21
LCM(420,819) = ( 420 × 819 ) / 21
LCM(420,819) = 343980 / 21
LCM(420,819) = 16380
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FAQs on GCF of Fractions of 178/420, 978/819
1. What is the HCF of 178,978?
The HCF of 178,978 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 178/420, 978/819?
Answer: GCF of Numerators as per given numbers 178/420, 978/819 is
GCF of Numerators i.e. for 178,978 is 2
LCM of denominators i.e. for 420,819 is 16380.
Thus, GCF of Fractions is 2/16380.Finally, GCF of Fractions for 178/420, 978/819 is 2/16380.