GCF of 190/430, 228/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 190/430, 228/978 i.e 38/210270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 190/430, 228/978.
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 190/430,228/978?
Given fractions are 190/430,228/978
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 190/430,228/978, numerators are 190,228
Denominators are 430,978
The GCF of 190,228 is 38 .
LCM of 430,978 is 210270.
The greatest common factor of 190/430,228/978 = [GCF of 190,228]/[LCM of 430,978]= 38/210270
Therefore, the GCF of 190/430,228/978 is 38/210270.
To find the highest common factor of 190,228, we have to find the factors of both numbers and list the highest common factor.
The factors of 190 are 1, 2, 5, 10, 19, 38, 95, 190
The factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
The HCF of 190,228 is 38.
Lets's calculate GCF of 190,228
| 2 | 190, 228 |
| 19 | 95, 114 |
| 5, 6 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 190,228 By Matching Biggest Common Factor Method
Now, list down the factors of 190
:1,2,5,10,19,38,95,190
Now, list down the factors of 228
:1,2,3,4,6,12,19,38,57,76,114,228
Greatest Common Factor
We found the factors 190,228 . The biggest common factor number is the GCF number.
So the greatest common factor 190,228 is 38.
Lets's calculate LCM of 430,978
| 2 | 430, 978 |
| 215, 489 |
∴ So the LCM of the given numbers is 2 x 215 x 489 = 210270
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/210270
Therefore, the GCF of Fractions 190/430,228/978 is 38/210270
Least Common Multiple of 430,978 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 430,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(430,978) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(430,978) x common factors =2 x 1 = 2
LCM(430,978) = ( 430 × 978 ) / 2
LCM(430,978) = 420540 / 2
LCM(430,978) = 210270
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 190/430, 228/978
1. What is the HCF of 190,228?
The HCF of 190,228 is 38
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 190/430, 228/978?
Answer: GCF of Numerators as per given numbers 190/430, 228/978 is
GCF of Numerators i.e. for 190,228 is 38
LCM of denominators i.e. for 430,978 is 210270.
Thus, GCF of Fractions is 38/210270.Finally, GCF of Fractions for 190/430, 228/978 is 38/210270.