Use our free GCF of Fractions Calculator tool to compute the GCF of 730/562, 380/278 i.e 10/78118 easily. The following is the detailed procedure to determine the greatest common factor of fractions 730/562, 380/278.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 730/562,380/278
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 730/562,380/278, numerators are 730,380
Denominators are 562,278
The GCF of 730,380 is 10 .
LCM of 562,278 is 78118.
The greatest common factor of 730/562,380/278 = [GCF of 730,380]/[LCM of 562,278]= 10/78118
Therefore, the GCF of 730/562,380/278 is 10/78118.
To find the highest common factor of 730,380, we have to find the factors of both numbers and list the highest common factor.
The factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730
The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
The HCF of 730,380 is 10.
Lets's calculate GCF of 730,380
2 | 730, 380 |
5 | 365, 190 |
73, 38 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 730
:1,2,5,10,73,146,365,730
Now, list down the factors of 380
:1,2,4,5,10,19,20,38,76,95,190,380
Greatest Common Factor
We found the factors 730,380 . The biggest common factor number is the GCF number.
So the greatest common factor 730,380 is 10.
Lets's calculate LCM of 562,278
2 | 562, 278 |
281, 139 |
∴ So the LCM of the given numbers is 2 x 281 x 139 = 78118
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/78118
Therefore, the GCF of Fractions 730/562,380/278 is 10/78118
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 562,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(562,278) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(562,278) x common factors =2 x 1 = 2
LCM(562,278) = ( 562 × 278 ) / 2
LCM(562,278) = 156236 / 2
LCM(562,278) = 78118
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 730,380?
The HCF of 730,380 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 730/562, 380/278?
Answer: GCF of Numerators as per given numbers 730/562, 380/278 is
GCF of Numerators i.e. for 730,380 is 10
LCM of denominators i.e. for 562,278 is 78118.
Thus, GCF of Fractions is 10/78118.Finally, GCF of Fractions for 730/562, 380/278 is 10/78118.