Use our free GCF of Fractions Calculator tool to compute the GCF of 674/980, 208/169 i.e 2/165620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 674/980, 208/169.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 674/980,208/169
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 674/980,208/169, numerators are 674,208
Denominators are 980,169
The GCF of 674,208 is 2 .
LCM of 980,169 is 165620.
The greatest common factor of 674/980,208/169 = [GCF of 674,208]/[LCM of 980,169]= 2/165620
Therefore, the GCF of 674/980,208/169 is 2/165620.
To find the highest common factor of 674,208, we have to find the factors of both numbers and list the highest common factor.
The factors of 674 are 1, 2, 337, 674
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The HCF of 674,208 is 2.
Lets's calculate GCF of 674,208
2 | 674, 208 |
337, 104 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 674
:1,2,337,674
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Greatest Common Factor
We found the factors 674,208 . The biggest common factor number is the GCF number.
So the greatest common factor 674,208 is 2.
Lets's calculate LCM of 980,169
Given numbers has no common factors except 1. So, there LCM is their product i.e 165620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/165620
Therefore, the GCF of Fractions 674/980,208/169 is 2/165620
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 980,169 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(980,169) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(980,169) x common factors =1 x 1 = 1
LCM(980,169) = ( 980 × 169 ) / 1
LCM(980,169) = 165620 / 1
LCM(980,169) = 165620
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 674,208?
The HCF of 674,208 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 674/980, 208/169?
Answer: GCF of Numerators as per given numbers 674/980, 208/169 is
GCF of Numerators i.e. for 674,208 is 2
LCM of denominators i.e. for 980,169 is 165620.
Thus, GCF of Fractions is 2/165620.Finally, GCF of Fractions for 674/980, 208/169 is 2/165620.