GCF of 7821/123, 7478/321
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7821/123, 7478/321 i.e 1/13161 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7821/123, 7478/321.
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 7821/123,7478/321?
Given fractions are 7821/123,7478/321
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 7821/123,7478/321, numerators are 7821,7478
Denominators are 123,321
The GCF of 7821,7478 is 1 .
LCM of 123,321 is 13161.
The greatest common factor of 7821/123,7478/321 = [GCF of 7821,7478]/[LCM of 123,321]= 1/13161
Therefore, the GCF of 7821/123,7478/321 is 1/13161.
To find the highest common factor of 7821,7478, we have to find the factors of both numbers and list the highest common factor.
The factors of 7821 are 1, 3, 9, 11, 33, 79, 99, 237, 711, 869, 2607, 7821
The factors of 7478 are 1, 2, 3739, 7478
The HCF of 7821,7478 is 1.
Lets's calculate GCF of 7821,7478
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7821,7478 By Matching Biggest Common Factor Method
Now, list down the factors of 7821
:1,3,9,11,33,79,99,237,711,869,2607,7821
Now, list down the factors of 7478
:1,2,3739,7478
Greatest Common Factor
We found the factors 7821,7478 . The biggest common factor number is the GCF number.
So the greatest common factor 7821,7478 is 1.
Lets's calculate LCM of 123,321
| 3 | 123, 321 |
| 41, 107 |
∴ So the LCM of the given numbers is 3 x 41 x 107 = 13161
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13161
Therefore, the GCF of Fractions 7821/123,7478/321 is 1/13161
Least Common Multiple of 123,321 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 123,321 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(123,321) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(123,321) x common factors =3 x 1 = 3
LCM(123,321) = ( 123 × 321 ) / 3
LCM(123,321) = 39483 / 3
LCM(123,321) = 13161
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FAQs on GCF of Fractions of 7821/123, 7478/321
1. What is the HCF of 7821,7478?
The HCF of 7821,7478 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 7821/123, 7478/321?
Answer: GCF of Numerators as per given numbers 7821/123, 7478/321 is
GCF of Numerators i.e. for 7821,7478 is 1
LCM of denominators i.e. for 123,321 is 13161.
Thus, GCF of Fractions is 1/13161.Finally, GCF of Fractions for 7821/123, 7478/321 is 1/13161.