Use our free GCF of Fractions Calculator tool to compute the GCF of 740/217, 590/283 i.e 10/61411 easily. The following is the detailed procedure to determine the greatest common factor of fractions 740/217, 590/283.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 740/217,590/283
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 740/217,590/283, numerators are 740,590
Denominators are 217,283
The GCF of 740,590 is 10 .
LCM of 217,283 is 61411.
The greatest common factor of 740/217,590/283 = [GCF of 740,590]/[LCM of 217,283]= 10/61411
Therefore, the GCF of 740/217,590/283 is 10/61411.
To find the highest common factor of 740,590, we have to find the factors of both numbers and list the highest common factor.
The factors of 740 are 1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740
The factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590
The HCF of 740,590 is 10.
Lets's calculate GCF of 740,590
2 | 740, 590 |
5 | 370, 295 |
74, 59 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 740
:1,2,4,5,10,20,37,74,148,185,370,740
Now, list down the factors of 590
:1,2,5,10,59,118,295,590
Greatest Common Factor
We found the factors 740,590 . The biggest common factor number is the GCF number.
So the greatest common factor 740,590 is 10.
Lets's calculate LCM of 217,283
Given numbers has no common factors except 1. So, there LCM is their product i.e 61411
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/61411
Therefore, the GCF of Fractions 740/217,590/283 is 10/61411
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 217,283 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,283) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(217,283) x common factors =1 x 1 = 1
LCM(217,283) = ( 217 × 283 ) / 1
LCM(217,283) = 61411 / 1
LCM(217,283) = 61411
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 740,590?
The HCF of 740,590 is 10
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 740/217, 590/283?
Answer: GCF of Numerators as per given numbers 740/217, 590/283 is
GCF of Numerators i.e. for 740,590 is 10
LCM of denominators i.e. for 217,283 is 61411.
Thus, GCF of Fractions is 10/61411.Finally, GCF of Fractions for 740/217, 590/283 is 10/61411.