Use our free GCF of Fractions Calculator tool to compute the GCF of 342/383, 984/707 i.e 6/270781 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/383, 984/707.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 342/383,984/707
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 342/383,984/707, numerators are 342,984
Denominators are 383,707
The GCF of 342,984 is 6 .
LCM of 383,707 is 270781.
The greatest common factor of 342/383,984/707 = [GCF of 342,984]/[LCM of 383,707]= 6/270781
Therefore, the GCF of 342/383,984/707 is 6/270781.
To find the highest common factor of 342,984, we have to find the factors of both numbers and list the highest common factor.
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984
The HCF of 342,984 is 6.
Lets's calculate GCF of 342,984
2 | 342, 984 |
3 | 171, 492 |
57, 164 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Now, list down the factors of 984
:1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984
Greatest Common Factor
We found the factors 342,984 . The biggest common factor number is the GCF number.
So the greatest common factor 342,984 is 6.
Lets's calculate LCM of 383,707
Given numbers has no common factors except 1. So, there LCM is their product i.e 270781
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/270781
Therefore, the GCF of Fractions 342/383,984/707 is 6/270781
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 383,707 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(383,707) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(383,707) x common factors =1 x 1 = 1
LCM(383,707) = ( 383 × 707 ) / 1
LCM(383,707) = 270781 / 1
LCM(383,707) = 270781
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 342,984?
The HCF of 342,984 is 6
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 342/383, 984/707?
Answer: GCF of Numerators as per given numbers 342/383, 984/707 is
GCF of Numerators i.e. for 342,984 is 6
LCM of denominators i.e. for 383,707 is 270781.
Thus, GCF of Fractions is 6/270781.Finally, GCF of Fractions for 342/383, 984/707 is 6/270781.