GCF of 305/408, 581/762
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 305/408, 581/762 i.e 1/51816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 305/408, 581/762.
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 305/408,581/762?
Given fractions are 305/408,581/762
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 305/408,581/762, numerators are 305,581
Denominators are 408,762
The GCF of 305,581 is 1 .
LCM of 408,762 is 51816.
The greatest common factor of 305/408,581/762 = [GCF of 305,581]/[LCM of 408,762]= 1/51816
Therefore, the GCF of 305/408,581/762 is 1/51816.
To find the highest common factor of 305,581, we have to find the factors of both numbers and list the highest common factor.
The factors of 305 are 1, 5, 61, 305
The factors of 581 are 1, 7, 83, 581
The HCF of 305,581 is 1.
Lets's calculate GCF of 305,581
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 305,581 By Matching Biggest Common Factor Method
Now, list down the factors of 305
:1,5,61,305
Now, list down the factors of 581
:1,7,83,581
Greatest Common Factor
We found the factors 305,581 . The biggest common factor number is the GCF number.
So the greatest common factor 305,581 is 1.
Lets's calculate LCM of 408,762
| 2 | 408, 762 |
| 3 | 204, 381 |
| 68, 127 |
∴ So the LCM of the given numbers is 2 x 3 x 68 x 127 = 51816
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/51816
Therefore, the GCF of Fractions 305/408,581/762 is 1/51816
Least Common Multiple of 408,762 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 408,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,762) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(408,762) x common factors =6 x 1 = 6
LCM(408,762) = ( 408 × 762 ) / 6
LCM(408,762) = 310896 / 6
LCM(408,762) = 51816
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FAQs on GCF of Fractions of 305/408, 581/762
1. What is the HCF of 305,581?
The HCF of 305,581 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 305/408, 581/762?
Answer: GCF of Numerators as per given numbers 305/408, 581/762 is
GCF of Numerators i.e. for 305,581 is 1
LCM of denominators i.e. for 408,762 is 51816.
Thus, GCF of Fractions is 1/51816.Finally, GCF of Fractions for 305/408, 581/762 is 1/51816.