GCF of 819/25, 312/5486
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 819/25, 312/5486 i.e 39/137150 easily. The following is the detailed procedure to determine the greatest common factor of fractions 819/25, 312/5486.
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 819/25,312/5486?
Given fractions are 819/25,312/5486
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 819/25,312/5486, numerators are 819,312
Denominators are 25,5486
The GCF of 819,312 is 39 .
LCM of 25,5486 is 137150.
The greatest common factor of 819/25,312/5486 = [GCF of 819,312]/[LCM of 25,5486]= 39/137150
Therefore, the GCF of 819/25,312/5486 is 39/137150.
To find the highest common factor of 819,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 819,312 is 39.
Lets's calculate GCF of 819,312
| 3 | 819, 312 |
| 13 | 273, 104 |
| 21, 8 |
∴ So the GCF of the given numbers is 3 x 13 = 39
Greatest Common Factor of 819,312 By Matching Biggest Common Factor Method
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 819,312 . The biggest common factor number is the GCF number.
So the greatest common factor 819,312 is 39.
Lets's calculate LCM of 25,5486
Given numbers has no common factors except 1. So, there LCM is their product i.e 137150
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 39/137150
Therefore, the GCF of Fractions 819/25,312/5486 is 39/137150
Least Common Multiple of 25,5486 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 25,5486 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(25,5486) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(25,5486) x common factors =1 x 1 = 1
LCM(25,5486) = ( 25 × 5486 ) / 1
LCM(25,5486) = 137150 / 1
LCM(25,5486) = 137150
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FAQs on GCF of Fractions of 819/25, 312/5486
1. What is the HCF of 819,312?
The HCF of 819,312 is 39
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 819/25, 312/5486?
Answer: GCF of Numerators as per given numbers 819/25, 312/5486 is
GCF of Numerators i.e. for 819,312 is 39
LCM of denominators i.e. for 25,5486 is 137150.
Thus, GCF of Fractions is 39/137150.Finally, GCF of Fractions for 819/25, 312/5486 is 39/137150.