Use our free GCF of Fractions Calculator tool to compute the GCF of 690/679, 698/210 i.e 2/20370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 690/679, 698/210.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 690/679,698/210
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 690/679,698/210, numerators are 690,698
Denominators are 679,210
The GCF of 690,698 is 2 .
LCM of 679,210 is 20370.
The greatest common factor of 690/679,698/210 = [GCF of 690,698]/[LCM of 679,210]= 2/20370
Therefore, the GCF of 690/679,698/210 is 2/20370.
To find the highest common factor of 690,698, we have to find the factors of both numbers and list the highest common factor.
The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
The factors of 698 are 1, 2, 349, 698
The HCF of 690,698 is 2.
Lets's calculate GCF of 690,698
2 | 690, 698 |
345, 349 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 690
:1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 690,698 . The biggest common factor number is the GCF number.
So the greatest common factor 690,698 is 2.
Lets's calculate LCM of 679,210
7 | 679, 210 |
97, 30 |
∴ So the LCM of the given numbers is 7 x 97 x 30 = 20370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/20370
Therefore, the GCF of Fractions 690/679,698/210 is 2/20370
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 679,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(679,210) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(679,210) x common factors =7 x 1 = 7
LCM(679,210) = ( 679 × 210 ) / 7
LCM(679,210) = 142590 / 7
LCM(679,210) = 20370
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 690,698?
The HCF of 690,698 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 690/679, 698/210?
Answer: GCF of Numerators as per given numbers 690/679, 698/210 is
GCF of Numerators i.e. for 690,698 is 2
LCM of denominators i.e. for 679,210 is 20370.
Thus, GCF of Fractions is 2/20370.Finally, GCF of Fractions for 690/679, 698/210 is 2/20370.