GCF of 577/545, 814/213, 524/413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 577/545, 814/213, 524/413 i.e 1/47943105 easily. The following is the detailed procedure to determine the greatest common factor of fractions 577/545, 814/213, 524/413.
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 577/545,814/213,524/413?
Given fractions are 577/545,814/213,524/413
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 577/545,814/213,524/413, numerators are 577,814,524
Denominators are 545,213,413
The GCF of 577,814,524 is 1 .
LCM of 545,213,413 is 47943105.
The greatest common factor of 577/545,814/213,524/413 = [GCF of 577,814,524]/[LCM of 545,213,413]= 1/47943105
Therefore, the GCF of 577/545,814/213,524/413 is 1/47943105.
To find the highest common factor of 577,814,524, we have to find the factors of both numbers and list the highest common factor.
The factors of 577 are 1, 577
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The factors of 524 are 1, 2, 4, 131, 262, 524
The HCF of 577,814,524 is 1.
Lets's calculate GCF of 577,814,524
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 577,814,524 By Matching Biggest Common Factor Method
Now, list down the factors of 577
:1,577
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Now, list down the factors of 524
:1,2,4,131,262,524
Greatest Common Factor
We found the factors 577,814,524 . The biggest common factor number is the GCF number.
So the greatest common factor 577,814,524 is 1.
Lets's calculate LCM of 545,213,413
Given numbers has no common factors except 1. So, there LCM is their product i.e 47943105
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/47943105
Therefore, the GCF of Fractions 577/545,814/213,524/413 is 1/47943105
Least Common Multiple of 545,213,413 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 545,213,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(545,213,413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(545,213,413) x common factors =1 x 1 = 1
LCM(545,213,413) = ( 545 × 213 × 413 ) / 1
LCM(545,213,413) = 47943105 / 1
LCM(545,213,413) = 47943105
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FAQs on GCF of Fractions of 577/545, 814/213, 524/413
1. What is the HCF of 577,814,524?
The HCF of 577,814,524 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 577/545, 814/213, 524/413?
Answer: GCF of Numerators as per given numbers 577/545, 814/213, 524/413 is
GCF of Numerators i.e. for 577,814,524 is 1
LCM of denominators i.e. for 545,213,413 is 47943105.
Thus, GCF of Fractions is 1/47943105.Finally, GCF of Fractions for 577/545, 814/213, 524/413 is 1/47943105.