Use our free GCF of Fractions Calculator tool to compute the GCF of 744/205, 846/667 i.e 6/136735 easily. The following is the detailed procedure to determine the greatest common factor of fractions 744/205, 846/667.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 744/205,846/667
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 744/205,846/667, numerators are 744,846
Denominators are 205,667
The GCF of 744,846 is 6 .
LCM of 205,667 is 136735.
The greatest common factor of 744/205,846/667 = [GCF of 744,846]/[LCM of 205,667]= 6/136735
Therefore, the GCF of 744/205,846/667 is 6/136735.
To find the highest common factor of 744,846, we have to find the factors of both numbers and list the highest common factor.
The factors of 744 are 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744
The factors of 846 are 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846
The HCF of 744,846 is 6.
Lets's calculate GCF of 744,846
2 | 744, 846 |
3 | 372, 423 |
124, 141 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 744
:1,2,3,4,6,8,12,24,31,62,93,124,186,248,372,744
Now, list down the factors of 846
:1,2,3,6,9,18,47,94,141,282,423,846
Greatest Common Factor
We found the factors 744,846 . The biggest common factor number is the GCF number.
So the greatest common factor 744,846 is 6.
Lets's calculate LCM of 205,667
Given numbers has no common factors except 1. So, there LCM is their product i.e 136735
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/136735
Therefore, the GCF of Fractions 744/205,846/667 is 6/136735
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 205,667 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,667) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,667) x common factors =1 x 1 = 1
LCM(205,667) = ( 205 × 667 ) / 1
LCM(205,667) = 136735 / 1
LCM(205,667) = 136735
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 744,846?
The HCF of 744,846 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 744/205, 846/667?
Answer: GCF of Numerators as per given numbers 744/205, 846/667 is
GCF of Numerators i.e. for 744,846 is 6
LCM of denominators i.e. for 205,667 is 136735.
Thus, GCF of Fractions is 6/136735.Finally, GCF of Fractions for 744/205, 846/667 is 6/136735.