GCF of 78/361, 82/208, 732/275
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 78/361, 82/208, 732/275 i.e 2/20649200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/361, 82/208, 732/275.
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 78/361,82/208,732/275?
Given fractions are 78/361,82/208,732/275
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 78/361,82/208,732/275, numerators are 78,82,732
Denominators are 361,208,275
The GCF of 78,82,732 is 2 .
LCM of 361,208,275 is 20649200.
The greatest common factor of 78/361,82/208,732/275 = [GCF of 78,82,732]/[LCM of 361,208,275]= 2/20649200
Therefore, the GCF of 78/361,82/208,732/275 is 2/20649200.
To find the highest common factor of 78,82,732, we have to find the factors of both numbers and list the highest common factor.
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 82 are 1, 2, 41, 82
The factors of 732 are 1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732
The HCF of 78,82,732 is 2.
Lets's calculate GCF of 78,82,732
| 2 | 78, 82, 732 |
| 39, 41, 366 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 78,82,732 By Matching Biggest Common Factor Method
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 732
:1,2,3,4,6,12,61,122,183,244,366,732
Greatest Common Factor
We found the factors 78,82,732 . The biggest common factor number is the GCF number.
So the greatest common factor 78,82,732 is 2.
Lets's calculate LCM of 361,208,275
Given numbers has no common factors except 1. So, there LCM is their product i.e 20649200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/20649200
Therefore, the GCF of Fractions 78/361,82/208,732/275 is 2/20649200
Least Common Multiple of 361,208,275 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 361,208,275 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(361,208,275) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(361,208,275) x common factors =1 x 1 = 1
LCM(361,208,275) = ( 361 × 208 × 275 ) / 1
LCM(361,208,275) = 20649200 / 1
LCM(361,208,275) = 20649200
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FAQs on GCF of Fractions of 78/361, 82/208, 732/275
1. What is the HCF of 78,82,732?
The HCF of 78,82,732 is 2
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 78/361, 82/208, 732/275?
Answer: GCF of Numerators as per given numbers 78/361, 82/208, 732/275 is
GCF of Numerators i.e. for 78,82,732 is 2
LCM of denominators i.e. for 361,208,275 is 20649200.
Thus, GCF of Fractions is 2/20649200.Finally, GCF of Fractions for 78/361, 82/208, 732/275 is 2/20649200.