Use our free GCF of Fractions Calculator tool to compute the GCF of 680/224, 218/754 i.e 2/84448 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/224, 218/754.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 680/224,218/754
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 680/224,218/754, numerators are 680,218
Denominators are 224,754
The GCF of 680,218 is 2 .
LCM of 224,754 is 84448.
The greatest common factor of 680/224,218/754 = [GCF of 680,218]/[LCM of 224,754]= 2/84448
Therefore, the GCF of 680/224,218/754 is 2/84448.
To find the highest common factor of 680,218, 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 218 are 1, 2, 109, 218
The HCF of 680,218 is 2.
Lets's calculate GCF of 680,218
2 | 680, 218 |
340, 109 |
∴ So the GCF of the given numbers is 2 = 2
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 218
:1,2,109,218
Greatest Common Factor
We found the factors 680,218 . The biggest common factor number is the GCF number.
So the greatest common factor 680,218 is 2.
Lets's calculate LCM of 224,754
2 | 224, 754 |
112, 377 |
∴ So the LCM of the given numbers is 2 x 112 x 377 = 84448
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/84448
Therefore, the GCF of Fractions 680/224,218/754 is 2/84448
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 224,754 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(224,754) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(224,754) x common factors =2 x 1 = 2
LCM(224,754) = ( 224 × 754 ) / 2
LCM(224,754) = 168896 / 2
LCM(224,754) = 84448
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 680,218?
The HCF of 680,218 is 2
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 680/224, 218/754?
Answer: GCF of Numerators as per given numbers 680/224, 218/754 is
GCF of Numerators i.e. for 680,218 is 2
LCM of denominators i.e. for 224,754 is 84448.
Thus, GCF of Fractions is 2/84448.Finally, GCF of Fractions for 680/224, 218/754 is 2/84448.