GCF of 813/140, 284/410
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 813/140, 284/410 i.e 1/5740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 813/140, 284/410.
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 813/140,284/410?
Given fractions are 813/140,284/410
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 813/140,284/410, numerators are 813,284
Denominators are 140,410
The GCF of 813,284 is 1 .
LCM of 140,410 is 5740.
The greatest common factor of 813/140,284/410 = [GCF of 813,284]/[LCM of 140,410]= 1/5740
Therefore, the GCF of 813/140,284/410 is 1/5740.
To find the highest common factor of 813,284, we have to find the factors of both numbers and list the highest common factor.
The factors of 813 are 1, 3, 271, 813
The factors of 284 are 1, 2, 4, 71, 142, 284
The HCF of 813,284 is 1.
Lets's calculate GCF of 813,284
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 813,284 By Matching Biggest Common Factor Method
Now, list down the factors of 813
:1,3,271,813
Now, list down the factors of 284
:1,2,4,71,142,284
Greatest Common Factor
We found the factors 813,284 . The biggest common factor number is the GCF number.
So the greatest common factor 813,284 is 1.
Lets's calculate LCM of 140,410
| 2 | 140, 410 |
| 5 | 70, 205 |
| 14, 41 |
∴ So the LCM of the given numbers is 2 x 5 x 14 x 41 = 5740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5740
Therefore, the GCF of Fractions 813/140,284/410 is 1/5740
Least Common Multiple of 140,410 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 140,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(140,410) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(140,410) x common factors =10 x 1 = 10
LCM(140,410) = ( 140 × 410 ) / 10
LCM(140,410) = 57400 / 10
LCM(140,410) = 5740
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FAQs on GCF of Fractions of 813/140, 284/410
1. What is the HCF of 813,284?
The HCF of 813,284 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 813/140, 284/410?
Answer: GCF of Numerators as per given numbers 813/140, 284/410 is
GCF of Numerators i.e. for 813,284 is 1
LCM of denominators i.e. for 140,410 is 5740.
Thus, GCF of Fractions is 1/5740.Finally, GCF of Fractions for 813/140, 284/410 is 1/5740.