GCF of 68/30, 197/32, 209/961
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 68/30, 197/32, 209/961 i.e 1/461280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/30, 197/32, 209/961.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 68/30,197/32,209/961?
Given fractions are 68/30,197/32,209/961
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 68/30,197/32,209/961, numerators are 68,197,209
Denominators are 30,32,961
The GCF of 68,197,209 is 1 .
LCM of 30,32,961 is 461280.
The greatest common factor of 68/30,197/32,209/961 = [GCF of 68,197,209]/[LCM of 30,32,961]= 1/461280
Therefore, the GCF of 68/30,197/32,209/961 is 1/461280.
To find the highest common factor of 68,197,209, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 197 are 1, 197
The factors of 209 are 1, 11, 19, 209
The HCF of 68,197,209 is 1.
Lets's calculate GCF of 68,197,209
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 68,197,209 By Matching Biggest Common Factor Method
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 197
:1,197
Now, list down the factors of 209
:1,11,19,209
Greatest Common Factor
We found the factors 68,197,209 . The biggest common factor number is the GCF number.
So the greatest common factor 68,197,209 is 1.
Lets's calculate LCM of 30,32,961
| 2 | 30, 32, 961 |
| 15, 16, 961 |
∴ So the LCM of the given numbers is 2 x 15 x 16 x 961 = 461280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/461280
Therefore, the GCF of Fractions 68/30,197/32,209/961 is 1/461280
Least Common Multiple of 30,32,961 with GCF Formula
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 30,32,961 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,32,961) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(30,32,961) x common factors =1 x 2 = 2
LCM(30,32,961) = ( 30 × 32 × 961 ) / 2
LCM(30,32,961) = 922560 / 2
LCM(30,32,961) = 461280
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FAQs on GCF of Fractions of 68/30, 197/32, 209/961
1. What is the HCF of 68,197,209?
The HCF of 68,197,209 is 1
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 68/30, 197/32, 209/961?
Answer: GCF of Numerators as per given numbers 68/30, 197/32, 209/961 is
GCF of Numerators i.e. for 68,197,209 is 1
LCM of denominators i.e. for 30,32,961 is 461280.
Thus, GCF of Fractions is 1/461280.Finally, GCF of Fractions for 68/30, 197/32, 209/961 is 1/461280.