GCF of 731/85, 309/460
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 731/85, 309/460 i.e 1/7820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 731/85, 309/460.
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 731/85,309/460?
Given fractions are 731/85,309/460
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 731/85,309/460, numerators are 731,309
Denominators are 85,460
The GCF of 731,309 is 1 .
LCM of 85,460 is 7820.
The greatest common factor of 731/85,309/460 = [GCF of 731,309]/[LCM of 85,460]= 1/7820
Therefore, the GCF of 731/85,309/460 is 1/7820.
To find the highest common factor of 731,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 731 are 1, 17, 43, 731
The factors of 309 are 1, 3, 103, 309
The HCF of 731,309 is 1.
Lets's calculate GCF of 731,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 731,309 By Matching Biggest Common Factor Method
Now, list down the factors of 731
:1,17,43,731
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 731,309 . The biggest common factor number is the GCF number.
So the greatest common factor 731,309 is 1.
Lets's calculate LCM of 85,460
| 5 | 85, 460 |
| 17, 92 |
∴ So the LCM of the given numbers is 5 x 17 x 92 = 7820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7820
Therefore, the GCF of Fractions 731/85,309/460 is 1/7820
Least Common Multiple of 85,460 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 85,460 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,460) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(85,460) x common factors =5 x 1 = 5
LCM(85,460) = ( 85 × 460 ) / 5
LCM(85,460) = 39100 / 5
LCM(85,460) = 7820
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FAQs on GCF of Fractions of 731/85, 309/460
1. What is the HCF of 731,309?
The HCF of 731,309 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 731/85, 309/460?
Answer: GCF of Numerators as per given numbers 731/85, 309/460 is
GCF of Numerators i.e. for 731,309 is 1
LCM of denominators i.e. for 85,460 is 7820.
Thus, GCF of Fractions is 1/7820.Finally, GCF of Fractions for 731/85, 309/460 is 1/7820.