Use our free GCF of Fractions Calculator tool to compute the GCF of 654/348, 489/870 i.e 3/1740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/348, 489/870.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 654/348,489/870
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 654/348,489/870, numerators are 654,489
Denominators are 348,870
The GCF of 654,489 is 3 .
LCM of 348,870 is 1740.
The greatest common factor of 654/348,489/870 = [GCF of 654,489]/[LCM of 348,870]= 3/1740
Therefore, the GCF of 654/348,489/870 is 3/1740.
To find the highest common factor of 654,489, we have to find the factors of both numbers and list the highest common factor.
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The factors of 489 are 1, 3, 163, 489
The HCF of 654,489 is 3.
Lets's calculate GCF of 654,489
3 | 654, 489 |
218, 163 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Now, list down the factors of 489
:1,3,163,489
Greatest Common Factor
We found the factors 654,489 . The biggest common factor number is the GCF number.
So the greatest common factor 654,489 is 3.
Lets's calculate LCM of 348,870
2 | 348, 870 |
3 | 174, 435 |
29 | 58, 145 |
2, 5 |
∴ So the LCM of the given numbers is 2 x 3 x 29 x 2 x 5 = 1740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1740
Therefore, the GCF of Fractions 654/348,489/870 is 3/1740
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 348,870 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(348,870) = 174
common factors(in case of two or more numbers have common factors) = 1
GCF(348,870) x common factors =174 x 1 = 174
LCM(348,870) = ( 348 × 870 ) / 174
LCM(348,870) = 302760 / 174
LCM(348,870) = 1740
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 654,489?
The HCF of 654,489 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 654/348, 489/870?
Answer: GCF of Numerators as per given numbers 654/348, 489/870 is
GCF of Numerators i.e. for 654,489 is 3
LCM of denominators i.e. for 348,870 is 1740.
Thus, GCF of Fractions is 3/1740.Finally, GCF of Fractions for 654/348, 489/870 is 3/1740.