GCF of 7131/219, 5762/3780
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7131/219, 5762/3780 i.e 1/275940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7131/219, 5762/3780.
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 7131/219,5762/3780?
Given fractions are 7131/219,5762/3780
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 7131/219,5762/3780, numerators are 7131,5762
Denominators are 219,3780
The GCF of 7131,5762 is 1 .
LCM of 219,3780 is 275940.
The greatest common factor of 7131/219,5762/3780 = [GCF of 7131,5762]/[LCM of 219,3780]= 1/275940
Therefore, the GCF of 7131/219,5762/3780 is 1/275940.
To find the highest common factor of 7131,5762, we have to find the factors of both numbers and list the highest common factor.
The factors of 7131 are 1, 3, 2377, 7131
The factors of 5762 are 1, 2, 43, 67, 86, 134, 2881, 5762
The HCF of 7131,5762 is 1.
Lets's calculate GCF of 7131,5762
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7131,5762 By Matching Biggest Common Factor Method
Now, list down the factors of 7131
:1,3,2377,7131
Now, list down the factors of 5762
:1,2,43,67,86,134,2881,5762
Greatest Common Factor
We found the factors 7131,5762 . The biggest common factor number is the GCF number.
So the greatest common factor 7131,5762 is 1.
Lets's calculate LCM of 219,3780
| 3 | 219, 3780 |
| 73, 1260 |
∴ So the LCM of the given numbers is 3 x 73 x 1260 = 275940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/275940
Therefore, the GCF of Fractions 7131/219,5762/3780 is 1/275940
Least Common Multiple of 219,3780 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 219,3780 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,3780) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(219,3780) x common factors =3 x 1 = 3
LCM(219,3780) = ( 219 × 3780 ) / 3
LCM(219,3780) = 827820 / 3
LCM(219,3780) = 275940
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FAQs on GCF of Fractions of 7131/219, 5762/3780
1. What is the HCF of 7131,5762?
The HCF of 7131,5762 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 7131/219, 5762/3780?
Answer: GCF of Numerators as per given numbers 7131/219, 5762/3780 is
GCF of Numerators i.e. for 7131,5762 is 1
LCM of denominators i.e. for 219,3780 is 275940.
Thus, GCF of Fractions is 1/275940.Finally, GCF of Fractions for 7131/219, 5762/3780 is 1/275940.