Use our free GCF of Fractions Calculator tool to compute the GCF of 690/449, 669/407 i.e 3/182743 easily. The following is the detailed procedure to determine the greatest common factor of fractions 690/449, 669/407.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 690/449,669/407
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 690/449,669/407, numerators are 690,669
Denominators are 449,407
The GCF of 690,669 is 3 .
LCM of 449,407 is 182743.
The greatest common factor of 690/449,669/407 = [GCF of 690,669]/[LCM of 449,407]= 3/182743
Therefore, the GCF of 690/449,669/407 is 3/182743.
To find the highest common factor of 690,669, 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 669 are 1, 3, 223, 669
The HCF of 690,669 is 3.
Lets's calculate GCF of 690,669
3 | 690, 669 |
230, 223 |
∴ So the GCF of the given numbers is 3 = 3
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 669
:1,3,223,669
Greatest Common Factor
We found the factors 690,669 . The biggest common factor number is the GCF number.
So the greatest common factor 690,669 is 3.
Lets's calculate LCM of 449,407
Given numbers has no common factors except 1. So, there LCM is their product i.e 182743
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/182743
Therefore, the GCF of Fractions 690/449,669/407 is 3/182743
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 449,407 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(449,407) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(449,407) x common factors =1 x 1 = 1
LCM(449,407) = ( 449 × 407 ) / 1
LCM(449,407) = 182743 / 1
LCM(449,407) = 182743
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 690,669?
The HCF of 690,669 is 3
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 690/449, 669/407?
Answer: GCF of Numerators as per given numbers 690/449, 669/407 is
GCF of Numerators i.e. for 690,669 is 3
LCM of denominators i.e. for 449,407 is 182743.
Thus, GCF of Fractions is 3/182743.Finally, GCF of Fractions for 690/449, 669/407 is 3/182743.