GCF of 1305/414, 1564/385
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1305/414, 1564/385 i.e 1/159390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1305/414, 1564/385.
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 1305/414,1564/385?
Given fractions are 1305/414,1564/385
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 1305/414,1564/385, numerators are 1305,1564
Denominators are 414,385
The GCF of 1305,1564 is 1 .
LCM of 414,385 is 159390.
The greatest common factor of 1305/414,1564/385 = [GCF of 1305,1564]/[LCM of 414,385]= 1/159390
Therefore, the GCF of 1305/414,1564/385 is 1/159390.
To find the highest common factor of 1305,1564, we have to find the factors of both numbers and list the highest common factor.
The factors of 1305 are 1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, 1305
The factors of 1564 are 1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, 1564
The HCF of 1305,1564 is 1.
Lets's calculate GCF of 1305,1564
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1305,1564 By Matching Biggest Common Factor Method
Now, list down the factors of 1305
:1,3,5,9,15,29,45,87,145,261,435,1305
Now, list down the factors of 1564
:1,2,4,17,23,34,46,68,92,391,782,1564
Greatest Common Factor
We found the factors 1305,1564 . The biggest common factor number is the GCF number.
So the greatest common factor 1305,1564 is 1.
Lets's calculate LCM of 414,385
Given numbers has no common factors except 1. So, there LCM is their product i.e 159390
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/159390
Therefore, the GCF of Fractions 1305/414,1564/385 is 1/159390
Least Common Multiple of 414,385 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 414,385 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,385) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(414,385) x common factors =1 x 1 = 1
LCM(414,385) = ( 414 × 385 ) / 1
LCM(414,385) = 159390 / 1
LCM(414,385) = 159390
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FAQs on GCF of Fractions of 1305/414, 1564/385
1. What is the HCF of 1305,1564?
The HCF of 1305,1564 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 1305/414, 1564/385?
Answer: GCF of Numerators as per given numbers 1305/414, 1564/385 is
GCF of Numerators i.e. for 1305,1564 is 1
LCM of denominators i.e. for 414,385 is 159390.
Thus, GCF of Fractions is 1/159390.Finally, GCF of Fractions for 1305/414, 1564/385 is 1/159390.