GCF of 821/299, 1954/253
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 821/299, 1954/253 i.e 1/3289 easily. The following is the detailed procedure to determine the greatest common factor of fractions 821/299, 1954/253.
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 821/299,1954/253?
Given fractions are 821/299,1954/253
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 821/299,1954/253, numerators are 821,1954
Denominators are 299,253
The GCF of 821,1954 is 1 .
LCM of 299,253 is 3289.
The greatest common factor of 821/299,1954/253 = [GCF of 821,1954]/[LCM of 299,253]= 1/3289
Therefore, the GCF of 821/299,1954/253 is 1/3289.
To find the highest common factor of 821,1954, we have to find the factors of both numbers and list the highest common factor.
The factors of 821 are 1, 821
The factors of 1954 are 1, 2, 977, 1954
The HCF of 821,1954 is 1.
Lets's calculate GCF of 821,1954
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 821,1954 By Matching Biggest Common Factor Method
Now, list down the factors of 821
:1,821
Now, list down the factors of 1954
:1,2,977,1954
Greatest Common Factor
We found the factors 821,1954 . The biggest common factor number is the GCF number.
So the greatest common factor 821,1954 is 1.
Lets's calculate LCM of 299,253
| 23 | 299, 253 |
| 13, 11 |
∴ So the LCM of the given numbers is 23 x 13 x 11 = 3289
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3289
Therefore, the GCF of Fractions 821/299,1954/253 is 1/3289
Least Common Multiple of 299,253 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 299,253 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(299,253) = 23
common factors(in case of two or more numbers have common factors) = 1
GCF(299,253) x common factors =23 x 1 = 23
LCM(299,253) = ( 299 × 253 ) / 23
LCM(299,253) = 75647 / 23
LCM(299,253) = 3289
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FAQs on GCF of Fractions of 821/299, 1954/253
1. What is the HCF of 821,1954?
The HCF of 821,1954 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 821/299, 1954/253?
Answer: GCF of Numerators as per given numbers 821/299, 1954/253 is
GCF of Numerators i.e. for 821,1954 is 1
LCM of denominators i.e. for 299,253 is 3289.
Thus, GCF of Fractions is 1/3289.Finally, GCF of Fractions for 821/299, 1954/253 is 1/3289.