GCF of 2074/311, 5314/7840
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2074/311, 5314/7840 i.e 2/2438240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2074/311, 5314/7840.
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 2074/311,5314/7840?
Given fractions are 2074/311,5314/7840
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 2074/311,5314/7840, numerators are 2074,5314
Denominators are 311,7840
The GCF of 2074,5314 is 2 .
LCM of 311,7840 is 2438240.
The greatest common factor of 2074/311,5314/7840 = [GCF of 2074,5314]/[LCM of 311,7840]= 2/2438240
Therefore, the GCF of 2074/311,5314/7840 is 2/2438240.
To find the highest common factor of 2074,5314, we have to find the factors of both numbers and list the highest common factor.
The factors of 2074 are 1, 2, 17, 34, 61, 122, 1037, 2074
The factors of 5314 are 1, 2, 2657, 5314
The HCF of 2074,5314 is 2.
Lets's calculate GCF of 2074,5314
| 2 | 2074, 5314 |
| 1037, 2657 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2074,5314 By Matching Biggest Common Factor Method
Now, list down the factors of 2074
:1,2,17,34,61,122,1037,2074
Now, list down the factors of 5314
:1,2,2657,5314
Greatest Common Factor
We found the factors 2074,5314 . The biggest common factor number is the GCF number.
So the greatest common factor 2074,5314 is 2.
Lets's calculate LCM of 311,7840
Given numbers has no common factors except 1. So, there LCM is their product i.e 2438240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2438240
Therefore, the GCF of Fractions 2074/311,5314/7840 is 2/2438240
Least Common Multiple of 311,7840 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 311,7840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(311,7840) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(311,7840) x common factors =1 x 1 = 1
LCM(311,7840) = ( 311 × 7840 ) / 1
LCM(311,7840) = 2438240 / 1
LCM(311,7840) = 2438240
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FAQs on GCF of Fractions of 2074/311, 5314/7840
1. What is the HCF of 2074,5314?
The HCF of 2074,5314 is 2
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 2074/311, 5314/7840?
Answer: GCF of Numerators as per given numbers 2074/311, 5314/7840 is
GCF of Numerators i.e. for 2074,5314 is 2
LCM of denominators i.e. for 311,7840 is 2438240.
Thus, GCF of Fractions is 2/2438240.Finally, GCF of Fractions for 2074/311, 5314/7840 is 2/2438240.