GCF of 1421/272, 5704/9814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1421/272, 5704/9814 i.e 1/1334704 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1421/272, 5704/9814.
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 1421/272,5704/9814?
Given fractions are 1421/272,5704/9814
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 1421/272,5704/9814, numerators are 1421,5704
Denominators are 272,9814
The GCF of 1421,5704 is 1 .
LCM of 272,9814 is 1334704.
The greatest common factor of 1421/272,5704/9814 = [GCF of 1421,5704]/[LCM of 272,9814]= 1/1334704
Therefore, the GCF of 1421/272,5704/9814 is 1/1334704.
To find the highest common factor of 1421,5704, we have to find the factors of both numbers and list the highest common factor.
The factors of 1421 are 1, 7, 29, 49, 203, 1421
The factors of 5704 are 1, 2, 4, 8, 23, 31, 46, 62, 92, 124, 184, 248, 713, 1426, 2852, 5704
The HCF of 1421,5704 is 1.
Lets's calculate GCF of 1421,5704
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1421,5704 By Matching Biggest Common Factor Method
Now, list down the factors of 1421
:1,7,29,49,203,1421
Now, list down the factors of 5704
:1,2,4,8,23,31,46,62,92,124,184,248,713,1426,2852,5704
Greatest Common Factor
We found the factors 1421,5704 . The biggest common factor number is the GCF number.
So the greatest common factor 1421,5704 is 1.
Lets's calculate LCM of 272,9814
| 2 | 272, 9814 |
| 136, 4907 |
∴ So the LCM of the given numbers is 2 x 136 x 4907 = 1334704
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1334704
Therefore, the GCF of Fractions 1421/272,5704/9814 is 1/1334704
Least Common Multiple of 272,9814 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 272,9814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(272,9814) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(272,9814) x common factors =2 x 1 = 2
LCM(272,9814) = ( 272 × 9814 ) / 2
LCM(272,9814) = 2669408 / 2
LCM(272,9814) = 1334704
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FAQs on GCF of Fractions of 1421/272, 5704/9814
1. What is the HCF of 1421,5704?
The HCF of 1421,5704 is 1
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 1421/272, 5704/9814?
Answer: GCF of Numerators as per given numbers 1421/272, 5704/9814 is
GCF of Numerators i.e. for 1421,5704 is 1
LCM of denominators i.e. for 272,9814 is 1334704.
Thus, GCF of Fractions is 1/1334704.Finally, GCF of Fractions for 1421/272, 5704/9814 is 1/1334704.