GCF of 8542/597, 7728/2082
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8542/597, 7728/2082 i.e 2/414318 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8542/597, 7728/2082.
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 8542/597,7728/2082?
Given fractions are 8542/597,7728/2082
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 8542/597,7728/2082, numerators are 8542,7728
Denominators are 597,2082
The GCF of 8542,7728 is 2 .
LCM of 597,2082 is 414318.
The greatest common factor of 8542/597,7728/2082 = [GCF of 8542,7728]/[LCM of 597,2082]= 2/414318
Therefore, the GCF of 8542/597,7728/2082 is 2/414318.
To find the highest common factor of 8542,7728, we have to find the factors of both numbers and list the highest common factor.
The factors of 8542 are 1, 2, 4271, 8542
The factors of 7728 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864, 7728
The HCF of 8542,7728 is 2.
Lets's calculate GCF of 8542,7728
| 2 | 8542, 7728 |
| 4271, 3864 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8542,7728 By Matching Biggest Common Factor Method
Now, list down the factors of 8542
:1,2,4271,8542
Now, list down the factors of 7728
:1,2,3,4,6,7,8,12,14,16,21,23,24,28,42,46,48,56,69,84,92,112,138,161,168,184,276,322,336,368,483,552,644,966,1104,1288,1932,2576,3864,7728
Greatest Common Factor
We found the factors 8542,7728 . The biggest common factor number is the GCF number.
So the greatest common factor 8542,7728 is 2.
Lets's calculate LCM of 597,2082
| 3 | 597, 2082 |
| 199, 694 |
∴ So the LCM of the given numbers is 3 x 199 x 694 = 414318
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/414318
Therefore, the GCF of Fractions 8542/597,7728/2082 is 2/414318
Least Common Multiple of 597,2082 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 597,2082 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(597,2082) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(597,2082) x common factors =3 x 1 = 3
LCM(597,2082) = ( 597 × 2082 ) / 3
LCM(597,2082) = 1242954 / 3
LCM(597,2082) = 414318
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FAQs on GCF of Fractions of 8542/597, 7728/2082
1. What is the HCF of 8542,7728?
The HCF of 8542,7728 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 8542/597, 7728/2082?
Answer: GCF of Numerators as per given numbers 8542/597, 7728/2082 is
GCF of Numerators i.e. for 8542,7728 is 2
LCM of denominators i.e. for 597,2082 is 414318.
Thus, GCF of Fractions is 2/414318.Finally, GCF of Fractions for 8542/597, 7728/2082 is 2/414318.