GCF of 1445/76, 8194/380
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1445/76, 8194/380 i.e 17/380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1445/76, 8194/380.
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 1445/76,8194/380?
Given fractions are 1445/76,8194/380
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 1445/76,8194/380, numerators are 1445,8194
Denominators are 76,380
The GCF of 1445,8194 is 17 .
LCM of 76,380 is 380.
The greatest common factor of 1445/76,8194/380 = [GCF of 1445,8194]/[LCM of 76,380]= 17/380
Therefore, the GCF of 1445/76,8194/380 is 17/380.
To find the highest common factor of 1445,8194, we have to find the factors of both numbers and list the highest common factor.
The factors of 1445 are 1, 5, 17, 85, 289, 1445
The factors of 8194 are 1, 2, 17, 34, 241, 482, 4097, 8194
The HCF of 1445,8194 is 17.
Lets's calculate GCF of 1445,8194
| 17 | 1445, 8194 |
| 85, 482 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 1445,8194 By Matching Biggest Common Factor Method
Now, list down the factors of 1445
:1,5,17,85,289,1445
Now, list down the factors of 8194
:1,2,17,34,241,482,4097,8194
Greatest Common Factor
We found the factors 1445,8194 . The biggest common factor number is the GCF number.
So the greatest common factor 1445,8194 is 17.
Lets's calculate LCM of 76,380
| 2 | 76, 380 |
| 2 | 38, 190 |
| 19 | 19, 95 |
| 1, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 19 x 1 x 5 = 380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/380
Therefore, the GCF of Fractions 1445/76,8194/380 is 17/380
Least Common Multiple of 76,380 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 76,380 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,380) = 76
common factors(in case of two or more numbers have common factors) = 1
GCF(76,380) x common factors =76 x 1 = 76
LCM(76,380) = ( 76 × 380 ) / 76
LCM(76,380) = 28880 / 76
LCM(76,380) = 380
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FAQs on GCF of Fractions of 1445/76, 8194/380
1. What is the HCF of 1445,8194?
The HCF of 1445,8194 is 17
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 1445/76, 8194/380?
Answer: GCF of Numerators as per given numbers 1445/76, 8194/380 is
GCF of Numerators i.e. for 1445,8194 is 17
LCM of denominators i.e. for 76,380 is 380.
Thus, GCF of Fractions is 17/380.Finally, GCF of Fractions for 1445/76, 8194/380 is 17/380.