GCF of 5457/512, 5211/8414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5457/512, 5211/8414 i.e 3/2153984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5457/512, 5211/8414.
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 5457/512,5211/8414?
Given fractions are 5457/512,5211/8414
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 5457/512,5211/8414, numerators are 5457,5211
Denominators are 512,8414
The GCF of 5457,5211 is 3 .
LCM of 512,8414 is 2153984.
The greatest common factor of 5457/512,5211/8414 = [GCF of 5457,5211]/[LCM of 512,8414]= 3/2153984
Therefore, the GCF of 5457/512,5211/8414 is 3/2153984.
To find the highest common factor of 5457,5211, we have to find the factors of both numbers and list the highest common factor.
The factors of 5457 are 1, 3, 17, 51, 107, 321, 1819, 5457
The factors of 5211 are 1, 3, 9, 27, 193, 579, 1737, 5211
The HCF of 5457,5211 is 3.
Lets's calculate GCF of 5457,5211
| 3 | 5457, 5211 |
| 1819, 1737 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 5457,5211 By Matching Biggest Common Factor Method
Now, list down the factors of 5457
:1,3,17,51,107,321,1819,5457
Now, list down the factors of 5211
:1,3,9,27,193,579,1737,5211
Greatest Common Factor
We found the factors 5457,5211 . The biggest common factor number is the GCF number.
So the greatest common factor 5457,5211 is 3.
Lets's calculate LCM of 512,8414
| 2 | 512, 8414 |
| 256, 4207 |
∴ So the LCM of the given numbers is 2 x 256 x 4207 = 2153984
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2153984
Therefore, the GCF of Fractions 5457/512,5211/8414 is 3/2153984
Least Common Multiple of 512,8414 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 512,8414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,8414) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(512,8414) x common factors =2 x 1 = 2
LCM(512,8414) = ( 512 × 8414 ) / 2
LCM(512,8414) = 4307968 / 2
LCM(512,8414) = 2153984
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FAQs on GCF of Fractions of 5457/512, 5211/8414
1. What is the HCF of 5457,5211?
The HCF of 5457,5211 is 3
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 5457/512, 5211/8414?
Answer: GCF of Numerators as per given numbers 5457/512, 5211/8414 is
GCF of Numerators i.e. for 5457,5211 is 3
LCM of denominators i.e. for 512,8414 is 2153984.
Thus, GCF of Fractions is 3/2153984.Finally, GCF of Fractions for 5457/512, 5211/8414 is 3/2153984.