Use our free GCF of Fractions Calculator tool to compute the GCF of 588/168, 109/672 i.e 1/672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 588/168, 109/672.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 588/168,109/672
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 588/168,109/672, numerators are 588,109
Denominators are 168,672
The GCF of 588,109 is 1 .
LCM of 168,672 is 672.
The greatest common factor of 588/168,109/672 = [GCF of 588,109]/[LCM of 168,672]= 1/672
Therefore, the GCF of 588/168,109/672 is 1/672.
To find the highest common factor of 588,109, we have to find the factors of both numbers and list the highest common factor.
The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
The factors of 109 are 1, 109
The HCF of 588,109 is 1.
Lets's calculate GCF of 588,109
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 588
:1,2,3,4,6,7,12,14,21,28,42,49,84,98,147,196,294,588
Now, list down the factors of 109
:1,109
Greatest Common Factor
We found the factors 588,109 . The biggest common factor number is the GCF number.
So the greatest common factor 588,109 is 1.
Lets's calculate LCM of 168,672
2 | 168, 672 |
2 | 84, 336 |
2 | 42, 168 |
3 | 21, 84 |
7 | 7, 28 |
1, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 7 x 1 x 4 = 672
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/672
Therefore, the GCF of Fractions 588/168,109/672 is 1/672
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 168,672 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(168,672) = 168
common factors(in case of two or more numbers have common factors) = 1
GCF(168,672) x common factors =168 x 1 = 168
LCM(168,672) = ( 168 × 672 ) / 168
LCM(168,672) = 112896 / 168
LCM(168,672) = 672
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 588,109?
The HCF of 588,109 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 588/168, 109/672?
Answer: GCF of Numerators as per given numbers 588/168, 109/672 is
GCF of Numerators i.e. for 588,109 is 1
LCM of denominators i.e. for 168,672 is 672.
Thus, GCF of Fractions is 1/672.Finally, GCF of Fractions for 588/168, 109/672 is 1/672.