GCF of 421/54, 617/182
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 421/54, 617/182 i.e 1/4914 easily. The following is the detailed procedure to determine the greatest common factor of fractions 421/54, 617/182.
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 421/54,617/182?
Given fractions are 421/54,617/182
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 421/54,617/182, numerators are 421,617
Denominators are 54,182
The GCF of 421,617 is 1 .
LCM of 54,182 is 4914.
The greatest common factor of 421/54,617/182 = [GCF of 421,617]/[LCM of 54,182]= 1/4914
Therefore, the GCF of 421/54,617/182 is 1/4914.
To find the highest common factor of 421,617, we have to find the factors of both numbers and list the highest common factor.
The factors of 421 are 1, 421
The factors of 617 are 1, 617
The HCF of 421,617 is 1.
Lets's calculate GCF of 421,617
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 421,617 By Matching Biggest Common Factor Method
Now, list down the factors of 421
:1,421
Now, list down the factors of 617
:1,617
Greatest Common Factor
We found the factors 421,617 . The biggest common factor number is the GCF number.
So the greatest common factor 421,617 is 1.
Lets's calculate LCM of 54,182
| 2 | 54, 182 |
| 27, 91 |
∴ So the LCM of the given numbers is 2 x 27 x 91 = 4914
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4914
Therefore, the GCF of Fractions 421/54,617/182 is 1/4914
Least Common Multiple of 54,182 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 54,182 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,182) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,182) x common factors =2 x 1 = 2
LCM(54,182) = ( 54 × 182 ) / 2
LCM(54,182) = 9828 / 2
LCM(54,182) = 4914
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 421/54, 617/182
1. What is the HCF of 421,617?
The HCF of 421,617 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 421/54, 617/182?
Answer: GCF of Numerators as per given numbers 421/54, 617/182 is
GCF of Numerators i.e. for 421,617 is 1
LCM of denominators i.e. for 54,182 is 4914.
Thus, GCF of Fractions is 1/4914.Finally, GCF of Fractions for 421/54, 617/182 is 1/4914.