GCF of 5314/723, 2785/6378
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5314/723, 2785/6378 i.e 1/1537098 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5314/723, 2785/6378.
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 5314/723,2785/6378?
Given fractions are 5314/723,2785/6378
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 5314/723,2785/6378, numerators are 5314,2785
Denominators are 723,6378
The GCF of 5314,2785 is 1 .
LCM of 723,6378 is 1537098.
The greatest common factor of 5314/723,2785/6378 = [GCF of 5314,2785]/[LCM of 723,6378]= 1/1537098
Therefore, the GCF of 5314/723,2785/6378 is 1/1537098.
To find the highest common factor of 5314,2785, we have to find the factors of both numbers and list the highest common factor.
The factors of 5314 are 1, 2, 2657, 5314
The factors of 2785 are 1, 5, 557, 2785
The HCF of 5314,2785 is 1.
Lets's calculate GCF of 5314,2785
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 5314,2785 By Matching Biggest Common Factor Method
Now, list down the factors of 5314
:1,2,2657,5314
Now, list down the factors of 2785
:1,5,557,2785
Greatest Common Factor
We found the factors 5314,2785 . The biggest common factor number is the GCF number.
So the greatest common factor 5314,2785 is 1.
Lets's calculate LCM of 723,6378
| 3 | 723, 6378 |
| 241, 2126 |
∴ So the LCM of the given numbers is 3 x 241 x 2126 = 1537098
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1537098
Therefore, the GCF of Fractions 5314/723,2785/6378 is 1/1537098
Least Common Multiple of 723,6378 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 723,6378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(723,6378) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(723,6378) x common factors =3 x 1 = 3
LCM(723,6378) = ( 723 × 6378 ) / 3
LCM(723,6378) = 4611294 / 3
LCM(723,6378) = 1537098
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FAQs on GCF of Fractions of 5314/723, 2785/6378
1. What is the HCF of 5314,2785?
The HCF of 5314,2785 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 5314/723, 2785/6378?
Answer: GCF of Numerators as per given numbers 5314/723, 2785/6378 is
GCF of Numerators i.e. for 5314,2785 is 1
LCM of denominators i.e. for 723,6378 is 1537098.
Thus, GCF of Fractions is 1/1537098.Finally, GCF of Fractions for 5314/723, 2785/6378 is 1/1537098.