Use our free GCF of Fractions Calculator tool to compute the GCF of 67/105, 49/109, 489/980 i.e 1/320460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 67/105, 49/109, 489/980.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 67/105,49/109,489/980
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 67/105,49/109,489/980, numerators are 67,49,489
Denominators are 105,109,980
The GCF of 67,49,489 is 1 .
LCM of 105,109,980 is 320460.
The greatest common factor of 67/105,49/109,489/980 = [GCF of 67,49,489]/[LCM of 105,109,980]= 1/320460
Therefore, the GCF of 67/105,49/109,489/980 is 1/320460.
To find the highest common factor of 67,49,489, we have to find the factors of both numbers and list the highest common factor.
The factors of 67 are 1, 67
The factors of 49 are 1, 7, 49
The factors of 489 are 1, 3, 163, 489
The HCF of 67,49,489 is 1.
Lets's calculate GCF of 67,49,489
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 67
:1,67
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 489
:1,3,163,489
Greatest Common Factor
We found the factors 67,49,489 . The biggest common factor number is the GCF number.
So the greatest common factor 67,49,489 is 1.
Lets's calculate LCM of 105,109,980
5 | 105, 109, 980 |
7 | 21, 109, 196 |
3, 109, 28 |
∴ So the LCM of the given numbers is 5 x 7 x 3 x 109 x 28 = 320460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/320460
Therefore, the GCF of Fractions 67/105,49/109,489/980 is 1/320460
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 105,109,980 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,109,980) = 1
common factors(in case of two or more numbers have common factors) = 35
GCF(105,109,980) x common factors =1 x 35 = 35
LCM(105,109,980) = ( 105 × 109 × 980 ) / 35
LCM(105,109,980) = 11216100 / 35
LCM(105,109,980) = 320460
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 67,49,489?
The HCF of 67,49,489 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 67/105, 49/109, 489/980?
Answer: GCF of Numerators as per given numbers 67/105, 49/109, 489/980 is
GCF of Numerators i.e. for 67,49,489 is 1
LCM of denominators i.e. for 105,109,980 is 320460.
Thus, GCF of Fractions is 1/320460.Finally, GCF of Fractions for 67/105, 49/109, 489/980 is 1/320460.