GCF of 79/185, 75/630, 306/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 79/185, 75/630, 306/814 i.e 1/256410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 79/185, 75/630, 306/814.
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 79/185,75/630,306/814?
Given fractions are 79/185,75/630,306/814
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 79/185,75/630,306/814, numerators are 79,75,306
Denominators are 185,630,814
The GCF of 79,75,306 is 1 .
LCM of 185,630,814 is 256410.
The greatest common factor of 79/185,75/630,306/814 = [GCF of 79,75,306]/[LCM of 185,630,814]= 1/256410
Therefore, the GCF of 79/185,75/630,306/814 is 1/256410.
To find the highest common factor of 79,75,306, we have to find the factors of both numbers and list the highest common factor.
The factors of 79 are 1, 79
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The HCF of 79,75,306 is 1.
Lets's calculate GCF of 79,75,306
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 79,75,306 By Matching Biggest Common Factor Method
Now, list down the factors of 79
:1,79
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Greatest Common Factor
We found the factors 79,75,306 . The biggest common factor number is the GCF number.
So the greatest common factor 79,75,306 is 1.
Lets's calculate LCM of 185,630,814
| 2 | 185, 630, 814 |
| 5 | 185, 315, 407 |
| 37 | 37, 63, 407 |
| 1, 63, 11 |
∴ So the LCM of the given numbers is 2 x 5 x 37 x 1 x 63 x 11 = 256410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/256410
Therefore, the GCF of Fractions 79/185,75/630,306/814 is 1/256410
Least Common Multiple of 185,630,814 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 185,630,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(185,630,814) = 1
common factors(in case of two or more numbers have common factors) = 370
GCF(185,630,814) x common factors =1 x 370 = 370
LCM(185,630,814) = ( 185 × 630 × 814 ) / 370
LCM(185,630,814) = 94871700 / 370
LCM(185,630,814) = 256410
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FAQs on GCF of Fractions of 79/185, 75/630, 306/814
1. What is the HCF of 79,75,306?
The HCF of 79,75,306 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 79/185, 75/630, 306/814?
Answer: GCF of Numerators as per given numbers 79/185, 75/630, 306/814 is
GCF of Numerators i.e. for 79,75,306 is 1
LCM of denominators i.e. for 185,630,814 is 256410.
Thus, GCF of Fractions is 1/256410.Finally, GCF of Fractions for 79/185, 75/630, 306/814 is 1/256410.