GCF of 1727/549, 6141/1728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1727/549, 6141/1728 i.e 1/105408 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1727/549, 6141/1728.
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 1727/549,6141/1728?
Given fractions are 1727/549,6141/1728
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 1727/549,6141/1728, numerators are 1727,6141
Denominators are 549,1728
The GCF of 1727,6141 is 1 .
LCM of 549,1728 is 105408.
The greatest common factor of 1727/549,6141/1728 = [GCF of 1727,6141]/[LCM of 549,1728]= 1/105408
Therefore, the GCF of 1727/549,6141/1728 is 1/105408.
To find the highest common factor of 1727,6141, we have to find the factors of both numbers and list the highest common factor.
The factors of 1727 are 1, 11, 157, 1727
The factors of 6141 are 1, 3, 23, 69, 89, 267, 2047, 6141
The HCF of 1727,6141 is 1.
Lets's calculate GCF of 1727,6141
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1727,6141 By Matching Biggest Common Factor Method
Now, list down the factors of 1727
:1,11,157,1727
Now, list down the factors of 6141
:1,3,23,69,89,267,2047,6141
Greatest Common Factor
We found the factors 1727,6141 . The biggest common factor number is the GCF number.
So the greatest common factor 1727,6141 is 1.
Lets's calculate LCM of 549,1728
| 3 | 549, 1728 |
| 3 | 183, 576 |
| 61, 192 |
∴ So the LCM of the given numbers is 3 x 3 x 61 x 192 = 105408
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/105408
Therefore, the GCF of Fractions 1727/549,6141/1728 is 1/105408
Least Common Multiple of 549,1728 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 549,1728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(549,1728) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(549,1728) x common factors =9 x 1 = 9
LCM(549,1728) = ( 549 × 1728 ) / 9
LCM(549,1728) = 948672 / 9
LCM(549,1728) = 105408
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FAQs on GCF of Fractions of 1727/549, 6141/1728
1. What is the HCF of 1727,6141?
The HCF of 1727,6141 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 1727/549, 6141/1728?
Answer: GCF of Numerators as per given numbers 1727/549, 6141/1728 is
GCF of Numerators i.e. for 1727,6141 is 1
LCM of denominators i.e. for 549,1728 is 105408.
Thus, GCF of Fractions is 1/105408.Finally, GCF of Fractions for 1727/549, 6141/1728 is 1/105408.