Use our free GCF of Fractions Calculator tool to compute the GCF of 669/509, 519/221 i.e 3/112489 easily. The following is the detailed procedure to determine the greatest common factor of fractions 669/509, 519/221.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 669/509,519/221
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 669/509,519/221, numerators are 669,519
Denominators are 509,221
The GCF of 669,519 is 3 .
LCM of 509,221 is 112489.
The greatest common factor of 669/509,519/221 = [GCF of 669,519]/[LCM of 509,221]= 3/112489
Therefore, the GCF of 669/509,519/221 is 3/112489.
To find the highest common factor of 669,519, we have to find the factors of both numbers and list the highest common factor.
The factors of 669 are 1, 3, 223, 669
The factors of 519 are 1, 3, 173, 519
The HCF of 669,519 is 3.
Lets's calculate GCF of 669,519
3 | 669, 519 |
223, 173 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 669
:1,3,223,669
Now, list down the factors of 519
:1,3,173,519
Greatest Common Factor
We found the factors 669,519 . The biggest common factor number is the GCF number.
So the greatest common factor 669,519 is 3.
Lets's calculate LCM of 509,221
Given numbers has no common factors except 1. So, there LCM is their product i.e 112489
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/112489
Therefore, the GCF of Fractions 669/509,519/221 is 3/112489
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 509,221 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(509,221) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(509,221) x common factors =1 x 1 = 1
LCM(509,221) = ( 509 × 221 ) / 1
LCM(509,221) = 112489 / 1
LCM(509,221) = 112489
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 669,519?
The HCF of 669,519 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 669/509, 519/221?
Answer: GCF of Numerators as per given numbers 669/509, 519/221 is
GCF of Numerators i.e. for 669,519 is 3
LCM of denominators i.e. for 509,221 is 112489.
Thus, GCF of Fractions is 3/112489.Finally, GCF of Fractions for 669/509, 519/221 is 3/112489.