GCF of 704/477, 3102/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 704/477, 3102/978 i.e 22/155502 easily. The following is the detailed procedure to determine the greatest common factor of fractions 704/477, 3102/978.
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 704/477,3102/978?
Given fractions are 704/477,3102/978
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 704/477,3102/978, numerators are 704,3102
Denominators are 477,978
The GCF of 704,3102 is 22 .
LCM of 477,978 is 155502.
The greatest common factor of 704/477,3102/978 = [GCF of 704,3102]/[LCM of 477,978]= 22/155502
Therefore, the GCF of 704/477,3102/978 is 22/155502.
To find the highest common factor of 704,3102, we have to find the factors of both numbers and list the highest common factor.
The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704
The factors of 3102 are 1, 2, 3, 6, 11, 22, 33, 47, 66, 94, 141, 282, 517, 1034, 1551, 3102
The HCF of 704,3102 is 22.
Lets's calculate GCF of 704,3102
| 2 | 704, 3102 |
| 11 | 352, 1551 |
| 32, 141 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 704,3102 By Matching Biggest Common Factor Method
Now, list down the factors of 704
:1,2,4,8,11,16,22,32,44,64,88,176,352,704
Now, list down the factors of 3102
:1,2,3,6,11,22,33,47,66,94,141,282,517,1034,1551,3102
Greatest Common Factor
We found the factors 704,3102 . The biggest common factor number is the GCF number.
So the greatest common factor 704,3102 is 22.
Lets's calculate LCM of 477,978
| 3 | 477, 978 |
| 159, 326 |
∴ So the LCM of the given numbers is 3 x 159 x 326 = 155502
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/155502
Therefore, the GCF of Fractions 704/477,3102/978 is 22/155502
Least Common Multiple of 477,978 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 477,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(477,978) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(477,978) x common factors =3 x 1 = 3
LCM(477,978) = ( 477 × 978 ) / 3
LCM(477,978) = 466506 / 3
LCM(477,978) = 155502
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FAQs on GCF of Fractions of 704/477, 3102/978
1. What is the HCF of 704,3102?
The HCF of 704,3102 is 22
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 704/477, 3102/978?
Answer: GCF of Numerators as per given numbers 704/477, 3102/978 is
GCF of Numerators i.e. for 704,3102 is 22
LCM of denominators i.e. for 477,978 is 155502.
Thus, GCF of Fractions is 22/155502.Finally, GCF of Fractions for 704/477, 3102/978 is 22/155502.