Use our free GCF of Fractions Calculator tool to compute the GCF of 476/546, 289/364 i.e 17/1092 easily. The following is the detailed procedure to determine the greatest common factor of fractions 476/546, 289/364.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 476/546,289/364
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 476/546,289/364, numerators are 476,289
Denominators are 546,364
The GCF of 476,289 is 17 .
LCM of 546,364 is 1092.
The greatest common factor of 476/546,289/364 = [GCF of 476,289]/[LCM of 546,364]= 17/1092
Therefore, the GCF of 476/546,289/364 is 17/1092.
To find the highest common factor of 476,289, we have to find the factors of both numbers and list the highest common factor.
The factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476
The factors of 289 are 1, 17, 289
The HCF of 476,289 is 17.
Lets's calculate GCF of 476,289
17 | 476, 289 |
28, 17 |
∴ So the GCF of the given numbers is 17 = 17
Now, list down the factors of 476
:1,2,4,7,14,17,28,34,68,119,238,476
Now, list down the factors of 289
:1,17,289
Greatest Common Factor
We found the factors 476,289 . The biggest common factor number is the GCF number.
So the greatest common factor 476,289 is 17.
Lets's calculate LCM of 546,364
2 | 546, 364 |
7 | 273, 182 |
13 | 39, 26 |
3, 2 |
∴ So the LCM of the given numbers is 2 x 7 x 13 x 3 x 2 = 1092
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/1092
Therefore, the GCF of Fractions 476/546,289/364 is 17/1092
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 546,364 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,364) = 182
common factors(in case of two or more numbers have common factors) = 1
GCF(546,364) x common factors =182 x 1 = 182
LCM(546,364) = ( 546 × 364 ) / 182
LCM(546,364) = 198744 / 182
LCM(546,364) = 1092
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 476,289?
The HCF of 476,289 is 17
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 476/546, 289/364?
Answer: GCF of Numerators as per given numbers 476/546, 289/364 is
GCF of Numerators i.e. for 476,289 is 17
LCM of denominators i.e. for 546,364 is 1092.
Thus, GCF of Fractions is 17/1092.Finally, GCF of Fractions for 476/546, 289/364 is 17/1092.