GCF of 643/816, 821/972
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 643/816, 821/972 i.e 1/66096 easily. The following is the detailed procedure to determine the greatest common factor of fractions 643/816, 821/972.
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 643/816,821/972?
Given fractions are 643/816,821/972
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 643/816,821/972, numerators are 643,821
Denominators are 816,972
The GCF of 643,821 is 1 .
LCM of 816,972 is 66096.
The greatest common factor of 643/816,821/972 = [GCF of 643,821]/[LCM of 816,972]= 1/66096
Therefore, the GCF of 643/816,821/972 is 1/66096.
To find the highest common factor of 643,821, we have to find the factors of both numbers and list the highest common factor.
The factors of 643 are 1, 643
The factors of 821 are 1, 821
The HCF of 643,821 is 1.
Lets's calculate GCF of 643,821
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 643,821 By Matching Biggest Common Factor Method
Now, list down the factors of 643
:1,643
Now, list down the factors of 821
:1,821
Greatest Common Factor
We found the factors 643,821 . The biggest common factor number is the GCF number.
So the greatest common factor 643,821 is 1.
Lets's calculate LCM of 816,972
| 2 | 816, 972 |
| 2 | 408, 486 |
| 3 | 204, 243 |
| 68, 81 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 68 x 81 = 66096
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/66096
Therefore, the GCF of Fractions 643/816,821/972 is 1/66096
Least Common Multiple of 816,972 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 816,972 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(816,972) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(816,972) x common factors =12 x 1 = 12
LCM(816,972) = ( 816 × 972 ) / 12
LCM(816,972) = 793152 / 12
LCM(816,972) = 66096
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FAQs on GCF of Fractions of 643/816, 821/972
1. What is the HCF of 643,821?
The HCF of 643,821 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 643/816, 821/972?
Answer: GCF of Numerators as per given numbers 643/816, 821/972 is
GCF of Numerators i.e. for 643,821 is 1
LCM of denominators i.e. for 816,972 is 66096.
Thus, GCF of Fractions is 1/66096.Finally, GCF of Fractions for 643/816, 821/972 is 1/66096.