GCF of 8421/378, 7416/8294
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8421/378, 7416/8294 i.e 3/1567566 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8421/378, 7416/8294.
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 8421/378,7416/8294?
Given fractions are 8421/378,7416/8294
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 8421/378,7416/8294, numerators are 8421,7416
Denominators are 378,8294
The GCF of 8421,7416 is 3 .
LCM of 378,8294 is 1567566.
The greatest common factor of 8421/378,7416/8294 = [GCF of 8421,7416]/[LCM of 378,8294]= 3/1567566
Therefore, the GCF of 8421/378,7416/8294 is 3/1567566.
To find the highest common factor of 8421,7416, we have to find the factors of both numbers and list the highest common factor.
The factors of 8421 are 1, 3, 7, 21, 401, 1203, 2807, 8421
The factors of 7416 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 103, 206, 309, 412, 618, 824, 927, 1236, 1854, 2472, 3708, 7416
The HCF of 8421,7416 is 3.
Lets's calculate GCF of 8421,7416
| 3 | 8421, 7416 |
| 2807, 2472 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 8421,7416 By Matching Biggest Common Factor Method
Now, list down the factors of 8421
:1,3,7,21,401,1203,2807,8421
Now, list down the factors of 7416
:1,2,3,4,6,8,9,12,18,24,36,72,103,206,309,412,618,824,927,1236,1854,2472,3708,7416
Greatest Common Factor
We found the factors 8421,7416 . The biggest common factor number is the GCF number.
So the greatest common factor 8421,7416 is 3.
Lets's calculate LCM of 378,8294
| 2 | 378, 8294 |
| 189, 4147 |
∴ So the LCM of the given numbers is 2 x 189 x 4147 = 1567566
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1567566
Therefore, the GCF of Fractions 8421/378,7416/8294 is 3/1567566
Least Common Multiple of 378,8294 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 378,8294 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,8294) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(378,8294) x common factors =2 x 1 = 2
LCM(378,8294) = ( 378 × 8294 ) / 2
LCM(378,8294) = 3135132 / 2
LCM(378,8294) = 1567566
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FAQs on GCF of Fractions of 8421/378, 7416/8294
1. What is the HCF of 8421,7416?
The HCF of 8421,7416 is 3
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 8421/378, 7416/8294?
Answer: GCF of Numerators as per given numbers 8421/378, 7416/8294 is
GCF of Numerators i.e. for 8421,7416 is 3
LCM of denominators i.e. for 378,8294 is 1567566.
Thus, GCF of Fractions is 3/1567566.Finally, GCF of Fractions for 8421/378, 7416/8294 is 3/1567566.