Use our free GCF of Fractions Calculator tool to compute the GCF of 210/454, 760/350 i.e 10/79450 easily. The following is the detailed procedure to determine the greatest common factor of fractions 210/454, 760/350.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 210/454,760/350
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 210/454,760/350, numerators are 210,760
Denominators are 454,350
The GCF of 210,760 is 10 .
LCM of 454,350 is 79450.
The greatest common factor of 210/454,760/350 = [GCF of 210,760]/[LCM of 454,350]= 10/79450
Therefore, the GCF of 210/454,760/350 is 10/79450.
To find the highest common factor of 210,760, we have to find the factors of both numbers and list the highest common factor.
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The HCF of 210,760 is 10.
Lets's calculate GCF of 210,760
2 | 210, 760 |
5 | 105, 380 |
21, 76 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Now, list down the factors of 760
:1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760
Greatest Common Factor
We found the factors 210,760 . The biggest common factor number is the GCF number.
So the greatest common factor 210,760 is 10.
Lets's calculate LCM of 454,350
2 | 454, 350 |
227, 175 |
∴ So the LCM of the given numbers is 2 x 227 x 175 = 79450
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/79450
Therefore, the GCF of Fractions 210/454,760/350 is 10/79450
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 454,350 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(454,350) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(454,350) x common factors =2 x 1 = 2
LCM(454,350) = ( 454 × 350 ) / 2
LCM(454,350) = 158900 / 2
LCM(454,350) = 79450
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 210,760?
The HCF of 210,760 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 210/454, 760/350?
Answer: GCF of Numerators as per given numbers 210/454, 760/350 is
GCF of Numerators i.e. for 210,760 is 10
LCM of denominators i.e. for 454,350 is 79450.
Thus, GCF of Fractions is 10/79450.Finally, GCF of Fractions for 210/454, 760/350 is 10/79450.