GCF of 821/71, 972/1731
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 821/71, 972/1731 i.e 1/122901 easily. The following is the detailed procedure to determine the greatest common factor of fractions 821/71, 972/1731.
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 821/71,972/1731?
Given fractions are 821/71,972/1731
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 821/71,972/1731, numerators are 821,972
Denominators are 71,1731
The GCF of 821,972 is 1 .
LCM of 71,1731 is 122901.
The greatest common factor of 821/71,972/1731 = [GCF of 821,972]/[LCM of 71,1731]= 1/122901
Therefore, the GCF of 821/71,972/1731 is 1/122901.
To find the highest common factor of 821,972, 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 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 821,972 is 1.
Lets's calculate GCF of 821,972
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 821,972 By Matching Biggest Common Factor Method
Now, list down the factors of 821
:1,821
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Greatest Common Factor
We found the factors 821,972 . The biggest common factor number is the GCF number.
So the greatest common factor 821,972 is 1.
Lets's calculate LCM of 71,1731
Given numbers has no common factors except 1. So, there LCM is their product i.e 122901
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/122901
Therefore, the GCF of Fractions 821/71,972/1731 is 1/122901
Least Common Multiple of 71,1731 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 71,1731 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,1731) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,1731) x common factors =1 x 1 = 1
LCM(71,1731) = ( 71 × 1731 ) / 1
LCM(71,1731) = 122901 / 1
LCM(71,1731) = 122901
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FAQs on GCF of Fractions of 821/71, 972/1731
1. What is the HCF of 821,972?
The HCF of 821,972 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 821/71, 972/1731?
Answer: GCF of Numerators as per given numbers 821/71, 972/1731 is
GCF of Numerators i.e. for 821,972 is 1
LCM of denominators i.e. for 71,1731 is 122901.
Thus, GCF of Fractions is 1/122901.Finally, GCF of Fractions for 821/71, 972/1731 is 1/122901.