Use our free GCF of Fractions Calculator tool to compute the GCF of 980/906, 144/217 i.e 4/196602 easily. The following is the detailed procedure to determine the greatest common factor of fractions 980/906, 144/217.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 980/906,144/217
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 980/906,144/217, numerators are 980,144
Denominators are 906,217
The GCF of 980,144 is 4 .
LCM of 906,217 is 196602.
The greatest common factor of 980/906,144/217 = [GCF of 980,144]/[LCM of 906,217]= 4/196602
Therefore, the GCF of 980/906,144/217 is 4/196602.
To find the highest common factor of 980,144, we have to find the factors of both numbers and list the highest common factor.
The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The HCF of 980,144 is 4.
Lets's calculate GCF of 980,144
2 | 980, 144 |
2 | 490, 72 |
245, 36 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 980
:1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Greatest Common Factor
We found the factors 980,144 . The biggest common factor number is the GCF number.
So the greatest common factor 980,144 is 4.
Lets's calculate LCM of 906,217
Given numbers has no common factors except 1. So, there LCM is their product i.e 196602
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/196602
Therefore, the GCF of Fractions 980/906,144/217 is 4/196602
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 906,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(906,217) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(906,217) x common factors =1 x 1 = 1
LCM(906,217) = ( 906 × 217 ) / 1
LCM(906,217) = 196602 / 1
LCM(906,217) = 196602
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 980,144?
The HCF of 980,144 is 4
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 980/906, 144/217?
Answer: GCF of Numerators as per given numbers 980/906, 144/217 is
GCF of Numerators i.e. for 980,144 is 4
LCM of denominators i.e. for 906,217 is 196602.
Thus, GCF of Fractions is 4/196602.Finally, GCF of Fractions for 980/906, 144/217 is 4/196602.