GCF of 493/208, 309/714
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 493/208, 309/714 i.e 1/74256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 493/208, 309/714.
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 493/208,309/714?
Given fractions are 493/208,309/714
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 493/208,309/714, numerators are 493,309
Denominators are 208,714
The GCF of 493,309 is 1 .
LCM of 208,714 is 74256.
The greatest common factor of 493/208,309/714 = [GCF of 493,309]/[LCM of 208,714]= 1/74256
Therefore, the GCF of 493/208,309/714 is 1/74256.
To find the highest common factor of 493,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 493 are 1, 17, 29, 493
The factors of 309 are 1, 3, 103, 309
The HCF of 493,309 is 1.
Lets's calculate GCF of 493,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 493,309 By Matching Biggest Common Factor Method
Now, list down the factors of 493
:1,17,29,493
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 493,309 . The biggest common factor number is the GCF number.
So the greatest common factor 493,309 is 1.
Lets's calculate LCM of 208,714
| 2 | 208, 714 |
| 104, 357 |
∴ So the LCM of the given numbers is 2 x 104 x 357 = 74256
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/74256
Therefore, the GCF of Fractions 493/208,309/714 is 1/74256
Least Common Multiple of 208,714 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 208,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,714) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(208,714) x common factors =2 x 1 = 2
LCM(208,714) = ( 208 × 714 ) / 2
LCM(208,714) = 148512 / 2
LCM(208,714) = 74256
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FAQs on GCF of Fractions of 493/208, 309/714
1. What is the HCF of 493,309?
The HCF of 493,309 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 493/208, 309/714?
Answer: GCF of Numerators as per given numbers 493/208, 309/714 is
GCF of Numerators i.e. for 493,309 is 1
LCM of denominators i.e. for 208,714 is 74256.
Thus, GCF of Fractions is 1/74256.Finally, GCF of Fractions for 493/208, 309/714 is 1/74256.