GCF of 307/408, 462/478
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 307/408, 462/478 i.e 1/97512 easily. The following is the detailed procedure to determine the greatest common factor of fractions 307/408, 462/478.
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 307/408,462/478?
Given fractions are 307/408,462/478
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 307/408,462/478, numerators are 307,462
Denominators are 408,478
The GCF of 307,462 is 1 .
LCM of 408,478 is 97512.
The greatest common factor of 307/408,462/478 = [GCF of 307,462]/[LCM of 408,478]= 1/97512
Therefore, the GCF of 307/408,462/478 is 1/97512.
To find the highest common factor of 307,462, we have to find the factors of both numbers and list the highest common factor.
The factors of 307 are 1, 307
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The HCF of 307,462 is 1.
Lets's calculate GCF of 307,462
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 307,462 By Matching Biggest Common Factor Method
Now, list down the factors of 307
:1,307
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Greatest Common Factor
We found the factors 307,462 . The biggest common factor number is the GCF number.
So the greatest common factor 307,462 is 1.
Lets's calculate LCM of 408,478
| 2 | 408, 478 |
| 204, 239 |
∴ So the LCM of the given numbers is 2 x 204 x 239 = 97512
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/97512
Therefore, the GCF of Fractions 307/408,462/478 is 1/97512
Least Common Multiple of 408,478 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 408,478 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,478) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(408,478) x common factors =2 x 1 = 2
LCM(408,478) = ( 408 × 478 ) / 2
LCM(408,478) = 195024 / 2
LCM(408,478) = 97512
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FAQs on GCF of Fractions of 307/408, 462/478
1. What is the HCF of 307,462?
The HCF of 307,462 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 307/408, 462/478?
Answer: GCF of Numerators as per given numbers 307/408, 462/478 is
GCF of Numerators i.e. for 307,462 is 1
LCM of denominators i.e. for 408,478 is 97512.
Thus, GCF of Fractions is 1/97512.Finally, GCF of Fractions for 307/408, 462/478 is 1/97512.