GCF of 82/31, 29/81, 980/837
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/31, 29/81, 980/837 i.e 1/2511 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/31, 29/81, 980/837.
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 82/31,29/81,980/837?
Given fractions are 82/31,29/81,980/837
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 82/31,29/81,980/837, numerators are 82,29,980
Denominators are 31,81,837
The GCF of 82,29,980 is 1 .
LCM of 31,81,837 is 2511.
The greatest common factor of 82/31,29/81,980/837 = [GCF of 82,29,980]/[LCM of 31,81,837]= 1/2511
Therefore, the GCF of 82/31,29/81,980/837 is 1/2511.
To find the highest common factor of 82,29,980, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 29 are 1, 29
The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
The HCF of 82,29,980 is 1.
Lets's calculate GCF of 82,29,980
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 82,29,980 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 29
:1,29
Now, list down the factors of 980
:1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980
Greatest Common Factor
We found the factors 82,29,980 . The biggest common factor number is the GCF number.
So the greatest common factor 82,29,980 is 1.
Lets's calculate LCM of 31,81,837
| 3 | 31, 81, 837 |
| 3 | 31, 27, 279 |
| 3 | 31, 9, 93 |
| 31 | 31, 3, 31 |
| 1, 3, 1 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 31 x 1 x 3 x 1 = 2511
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2511
Therefore, the GCF of Fractions 82/31,29/81,980/837 is 1/2511
Least Common Multiple of 31,81,837 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 31,81,837 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,81,837) = 1
common factors(in case of two or more numbers have common factors) = 837
GCF(31,81,837) x common factors =1 x 837 = 837
LCM(31,81,837) = ( 31 × 81 × 837 ) / 837
LCM(31,81,837) = 2101707 / 837
LCM(31,81,837) = 2511
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FAQs on GCF of Fractions of 82/31, 29/81, 980/837
1. What is the HCF of 82,29,980?
The HCF of 82,29,980 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 82/31, 29/81, 980/837?
Answer: GCF of Numerators as per given numbers 82/31, 29/81, 980/837 is
GCF of Numerators i.e. for 82,29,980 is 1
LCM of denominators i.e. for 31,81,837 is 2511.
Thus, GCF of Fractions is 1/2511.Finally, GCF of Fractions for 82/31, 29/81, 980/837 is 1/2511.