Use our free GCF of Fractions Calculator tool to compute the GCF of 680/223, 710/252 i.e 10/56196 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/223, 710/252.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 680/223,710/252
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 680/223,710/252, numerators are 680,710
Denominators are 223,252
The GCF of 680,710 is 10 .
LCM of 223,252 is 56196.
The greatest common factor of 680/223,710/252 = [GCF of 680,710]/[LCM of 223,252]= 10/56196
Therefore, the GCF of 680/223,710/252 is 10/56196.
To find the highest common factor of 680,710, we have to find the factors of both numbers and list the highest common factor.
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The factors of 710 are 1, 2, 5, 10, 71, 142, 355, 710
The HCF of 680,710 is 10.
Lets's calculate GCF of 680,710
2 | 680, 710 |
5 | 340, 355 |
68, 71 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Now, list down the factors of 710
:1,2,5,10,71,142,355,710
Greatest Common Factor
We found the factors 680,710 . The biggest common factor number is the GCF number.
So the greatest common factor 680,710 is 10.
Lets's calculate LCM of 223,252
Given numbers has no common factors except 1. So, there LCM is their product i.e 56196
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/56196
Therefore, the GCF of Fractions 680/223,710/252 is 10/56196
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 223,252 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(223,252) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(223,252) x common factors =1 x 1 = 1
LCM(223,252) = ( 223 × 252 ) / 1
LCM(223,252) = 56196 / 1
LCM(223,252) = 56196
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 680,710?
The HCF of 680,710 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 680/223, 710/252?
Answer: GCF of Numerators as per given numbers 680/223, 710/252 is
GCF of Numerators i.e. for 680,710 is 10
LCM of denominators i.e. for 223,252 is 56196.
Thus, GCF of Fractions is 10/56196.Finally, GCF of Fractions for 680/223, 710/252 is 10/56196.