GCF of 831/76, 742/5780
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 831/76, 742/5780 i.e 1/109820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 831/76, 742/5780.
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 831/76,742/5780?
Given fractions are 831/76,742/5780
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 831/76,742/5780, numerators are 831,742
Denominators are 76,5780
The GCF of 831,742 is 1 .
LCM of 76,5780 is 109820.
The greatest common factor of 831/76,742/5780 = [GCF of 831,742]/[LCM of 76,5780]= 1/109820
Therefore, the GCF of 831/76,742/5780 is 1/109820.
To find the highest common factor of 831,742, we have to find the factors of both numbers and list the highest common factor.
The factors of 831 are 1, 3, 277, 831
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The HCF of 831,742 is 1.
Lets's calculate GCF of 831,742
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 831,742 By Matching Biggest Common Factor Method
Now, list down the factors of 831
:1,3,277,831
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 831,742 . The biggest common factor number is the GCF number.
So the greatest common factor 831,742 is 1.
Lets's calculate LCM of 76,5780
| 2 | 76, 5780 |
| 2 | 38, 2890 |
| 19, 1445 |
∴ So the LCM of the given numbers is 2 x 2 x 19 x 1445 = 109820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/109820
Therefore, the GCF of Fractions 831/76,742/5780 is 1/109820
Least Common Multiple of 76,5780 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 76,5780 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,5780) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(76,5780) x common factors =4 x 1 = 4
LCM(76,5780) = ( 76 × 5780 ) / 4
LCM(76,5780) = 439280 / 4
LCM(76,5780) = 109820
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FAQs on GCF of Fractions of 831/76, 742/5780
1. What is the HCF of 831,742?
The HCF of 831,742 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 831/76, 742/5780?
Answer: GCF of Numerators as per given numbers 831/76, 742/5780 is
GCF of Numerators i.e. for 831,742 is 1
LCM of denominators i.e. for 76,5780 is 109820.
Thus, GCF of Fractions is 1/109820.Finally, GCF of Fractions for 831/76, 742/5780 is 1/109820.