GCF of 286/312, 583/769
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 286/312, 583/769 i.e 11/239928 easily. The following is the detailed procedure to determine the greatest common factor of fractions 286/312, 583/769.
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 286/312,583/769?
Given fractions are 286/312,583/769
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 286/312,583/769, numerators are 286,583
Denominators are 312,769
The GCF of 286,583 is 11 .
LCM of 312,769 is 239928.
The greatest common factor of 286/312,583/769 = [GCF of 286,583]/[LCM of 312,769]= 11/239928
Therefore, the GCF of 286/312,583/769 is 11/239928.
To find the highest common factor of 286,583, we have to find the factors of both numbers and list the highest common factor.
The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286
The factors of 583 are 1, 11, 53, 583
The HCF of 286,583 is 11.
Lets's calculate GCF of 286,583
| 11 | 286, 583 |
| 26, 53 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 286,583 By Matching Biggest Common Factor Method
Now, list down the factors of 286
:1,2,11,13,22,26,143,286
Now, list down the factors of 583
:1,11,53,583
Greatest Common Factor
We found the factors 286,583 . The biggest common factor number is the GCF number.
So the greatest common factor 286,583 is 11.
Lets's calculate LCM of 312,769
Given numbers has no common factors except 1. So, there LCM is their product i.e 239928
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/239928
Therefore, the GCF of Fractions 286/312,583/769 is 11/239928
Least Common Multiple of 312,769 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 312,769 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,769) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(312,769) x common factors =1 x 1 = 1
LCM(312,769) = ( 312 × 769 ) / 1
LCM(312,769) = 239928 / 1
LCM(312,769) = 239928
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FAQs on GCF of Fractions of 286/312, 583/769
1. What is the HCF of 286,583?
The HCF of 286,583 is 11
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 286/312, 583/769?
Answer: GCF of Numerators as per given numbers 286/312, 583/769 is
GCF of Numerators i.e. for 286,583 is 11
LCM of denominators i.e. for 312,769 is 239928.
Thus, GCF of Fractions is 11/239928.Finally, GCF of Fractions for 286/312, 583/769 is 11/239928.