GCF of 8140/194, 3663/768
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8140/194, 3663/768 i.e 407/74496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8140/194, 3663/768.
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 8140/194,3663/768?
Given fractions are 8140/194,3663/768
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 8140/194,3663/768, numerators are 8140,3663
Denominators are 194,768
The GCF of 8140,3663 is 407 .
LCM of 194,768 is 74496.
The greatest common factor of 8140/194,3663/768 = [GCF of 8140,3663]/[LCM of 194,768]= 407/74496
Therefore, the GCF of 8140/194,3663/768 is 407/74496.
To find the highest common factor of 8140,3663, we have to find the factors of both numbers and list the highest common factor.
The factors of 8140 are 1, 2, 4, 5, 10, 11, 20, 22, 37, 44, 55, 74, 110, 148, 185, 220, 370, 407, 740, 814, 1628, 2035, 4070, 8140
The factors of 3663 are 1, 3, 9, 11, 33, 37, 99, 111, 333, 407, 1221, 3663
The HCF of 8140,3663 is 407.
Lets's calculate GCF of 8140,3663
| 11 | 8140, 3663 |
| 37 | 740, 333 |
| 20, 9 |
∴ So the GCF of the given numbers is 11 x 37 = 407
Greatest Common Factor of 8140,3663 By Matching Biggest Common Factor Method
Now, list down the factors of 8140
:1,2,4,5,10,11,20,22,37,44,55,74,110,148,185,220,370,407,740,814,1628,2035,4070,8140
Now, list down the factors of 3663
:1,3,9,11,33,37,99,111,333,407,1221,3663
Greatest Common Factor
We found the factors 8140,3663 . The biggest common factor number is the GCF number.
So the greatest common factor 8140,3663 is 407.
Lets's calculate LCM of 194,768
| 2 | 194, 768 |
| 97, 384 |
∴ So the LCM of the given numbers is 2 x 97 x 384 = 74496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 407/74496
Therefore, the GCF of Fractions 8140/194,3663/768 is 407/74496
Least Common Multiple of 194,768 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 194,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(194,768) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(194,768) x common factors =2 x 1 = 2
LCM(194,768) = ( 194 × 768 ) / 2
LCM(194,768) = 148992 / 2
LCM(194,768) = 74496
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FAQs on GCF of Fractions of 8140/194, 3663/768
1. What is the HCF of 8140,3663?
The HCF of 8140,3663 is 407
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 8140/194, 3663/768?
Answer: GCF of Numerators as per given numbers 8140/194, 3663/768 is
GCF of Numerators i.e. for 8140,3663 is 407
LCM of denominators i.e. for 194,768 is 74496.
Thus, GCF of Fractions is 407/74496.Finally, GCF of Fractions for 8140/194, 3663/768 is 407/74496.