GCF of 203/304, 406/874
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 203/304, 406/874 i.e 203/6992 easily. The following is the detailed procedure to determine the greatest common factor of fractions 203/304, 406/874.
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 203/304,406/874?
Given fractions are 203/304,406/874
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 203/304,406/874, numerators are 203,406
Denominators are 304,874
The GCF of 203,406 is 203 .
LCM of 304,874 is 6992.
The greatest common factor of 203/304,406/874 = [GCF of 203,406]/[LCM of 304,874]= 203/6992
Therefore, the GCF of 203/304,406/874 is 203/6992.
To find the highest common factor of 203,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 203 are 1, 7, 29, 203
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 203,406 is 203.
Lets's calculate GCF of 203,406
| 7 | 203, 406 |
| 29 | 29, 58 |
| 1, 2 |
∴ So the GCF of the given numbers is 7 x 29 = 203
Greatest Common Factor of 203,406 By Matching Biggest Common Factor Method
Now, list down the factors of 203
:1,7,29,203
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 203,406 . The biggest common factor number is the GCF number.
So the greatest common factor 203,406 is 203.
Lets's calculate LCM of 304,874
| 2 | 304, 874 |
| 19 | 152, 437 |
| 8, 23 |
∴ So the LCM of the given numbers is 2 x 19 x 8 x 23 = 6992
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 203/6992
Therefore, the GCF of Fractions 203/304,406/874 is 203/6992
Least Common Multiple of 304,874 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 304,874 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(304,874) = 38
common factors(in case of two or more numbers have common factors) = 1
GCF(304,874) x common factors =38 x 1 = 38
LCM(304,874) = ( 304 × 874 ) / 38
LCM(304,874) = 265696 / 38
LCM(304,874) = 6992
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FAQs on GCF of Fractions of 203/304, 406/874
1. What is the HCF of 203,406?
The HCF of 203,406 is 203
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 203/304, 406/874?
Answer: GCF of Numerators as per given numbers 203/304, 406/874 is
GCF of Numerators i.e. for 203,406 is 203
LCM of denominators i.e. for 304,874 is 6992.
Thus, GCF of Fractions is 203/6992.Finally, GCF of Fractions for 203/304, 406/874 is 203/6992.