GCF of 721/194, 406/305
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 721/194, 406/305 i.e 7/59170 easily. The following is the detailed procedure to determine the greatest common factor of fractions 721/194, 406/305.
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 721/194,406/305?
Given fractions are 721/194,406/305
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 721/194,406/305, numerators are 721,406
Denominators are 194,305
The GCF of 721,406 is 7 .
LCM of 194,305 is 59170.
The greatest common factor of 721/194,406/305 = [GCF of 721,406]/[LCM of 194,305]= 7/59170
Therefore, the GCF of 721/194,406/305 is 7/59170.
To find the highest common factor of 721,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 721 are 1, 7, 103, 721
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 721,406 is 7.
Lets's calculate GCF of 721,406
| 7 | 721, 406 |
| 103, 58 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 721,406 By Matching Biggest Common Factor Method
Now, list down the factors of 721
:1,7,103,721
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 721,406 . The biggest common factor number is the GCF number.
So the greatest common factor 721,406 is 7.
Lets's calculate LCM of 194,305
Given numbers has no common factors except 1. So, there LCM is their product i.e 59170
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/59170
Therefore, the GCF of Fractions 721/194,406/305 is 7/59170
Least Common Multiple of 194,305 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 194,305 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(194,305) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(194,305) x common factors =1 x 1 = 1
LCM(194,305) = ( 194 × 305 ) / 1
LCM(194,305) = 59170 / 1
LCM(194,305) = 59170
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FAQs on GCF of Fractions of 721/194, 406/305
1. What is the HCF of 721,406?
The HCF of 721,406 is 7
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 721/194, 406/305?
Answer: GCF of Numerators as per given numbers 721/194, 406/305 is
GCF of Numerators i.e. for 721,406 is 7
LCM of denominators i.e. for 194,305 is 59170.
Thus, GCF of Fractions is 7/59170.Finally, GCF of Fractions for 721/194, 406/305 is 7/59170.