GCF of 71/298, 49/180, 981/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 71/298, 49/180, 981/414 i.e 1/616860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/298, 49/180, 981/414.
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 71/298,49/180,981/414?
Given fractions are 71/298,49/180,981/414
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 71/298,49/180,981/414, numerators are 71,49,981
Denominators are 298,180,414
The GCF of 71,49,981 is 1 .
LCM of 298,180,414 is 616860.
The greatest common factor of 71/298,49/180,981/414 = [GCF of 71,49,981]/[LCM of 298,180,414]= 1/616860
Therefore, the GCF of 71/298,49/180,981/414 is 1/616860.
To find the highest common factor of 71,49,981, we have to find the factors of both numbers and list the highest common factor.
The factors of 71 are 1, 71
The factors of 49 are 1, 7, 49
The factors of 981 are 1, 3, 9, 109, 327, 981
The HCF of 71,49,981 is 1.
Lets's calculate GCF of 71,49,981
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 71,49,981 By Matching Biggest Common Factor Method
Now, list down the factors of 71
:1,71
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 981
:1,3,9,109,327,981
Greatest Common Factor
We found the factors 71,49,981 . The biggest common factor number is the GCF number.
So the greatest common factor 71,49,981 is 1.
Lets's calculate LCM of 298,180,414
| 2 | 298, 180, 414 |
| 3 | 149, 90, 207 |
| 3 | 149, 30, 69 |
| 149, 10, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 149 x 10 x 23 = 616860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/616860
Therefore, the GCF of Fractions 71/298,49/180,981/414 is 1/616860
Least Common Multiple of 298,180,414 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 298,180,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(298,180,414) = 2
common factors(in case of two or more numbers have common factors) = 18
GCF(298,180,414) x common factors =2 x 18 = 36
LCM(298,180,414) = ( 298 × 180 × 414 ) / 36
LCM(298,180,414) = 22206960 / 36
LCM(298,180,414) = 616860
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FAQs on GCF of Fractions of 71/298, 49/180, 981/414
1. What is the HCF of 71,49,981?
The HCF of 71,49,981 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 71/298, 49/180, 981/414?
Answer: GCF of Numerators as per given numbers 71/298, 49/180, 981/414 is
GCF of Numerators i.e. for 71,49,981 is 1
LCM of denominators i.e. for 298,180,414 is 616860.
Thus, GCF of Fractions is 1/616860.Finally, GCF of Fractions for 71/298, 49/180, 981/414 is 1/616860.