GCF of 82/102, 861/778
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/102, 861/778 i.e 41/39678 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/102, 861/778.
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 82/102,861/778?
Given fractions are 82/102,861/778
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 82/102,861/778, numerators are 82,861
Denominators are 102,778
The GCF of 82,861 is 41 .
LCM of 102,778 is 39678.
The greatest common factor of 82/102,861/778 = [GCF of 82,861]/[LCM of 102,778]= 41/39678
Therefore, the GCF of 82/102,861/778 is 41/39678.
To find the highest common factor of 82,861, 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 861 are 1, 3, 7, 21, 41, 123, 287, 861
The HCF of 82,861 is 41.
Lets's calculate GCF of 82,861
| 41 | 82, 861 |
| 2, 21 |
∴ So the GCF of the given numbers is 41 = 41
Greatest Common Factor of 82,861 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 861
:1,3,7,21,41,123,287,861
Greatest Common Factor
We found the factors 82,861 . The biggest common factor number is the GCF number.
So the greatest common factor 82,861 is 41.
Lets's calculate LCM of 102,778
| 2 | 102, 778 |
| 51, 389 |
∴ So the LCM of the given numbers is 2 x 51 x 389 = 39678
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 41/39678
Therefore, the GCF of Fractions 82/102,861/778 is 41/39678
Least Common Multiple of 102,778 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 102,778 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(102,778) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(102,778) x common factors =2 x 1 = 2
LCM(102,778) = ( 102 × 778 ) / 2
LCM(102,778) = 79356 / 2
LCM(102,778) = 39678
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FAQs on GCF of Fractions of 82/102, 861/778
1. What is the HCF of 82,861?
The HCF of 82,861 is 41
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 82/102, 861/778?
Answer: GCF of Numerators as per given numbers 82/102, 861/778 is
GCF of Numerators i.e. for 82,861 is 41
LCM of denominators i.e. for 102,778 is 39678.
Thus, GCF of Fractions is 41/39678.Finally, GCF of Fractions for 82/102, 861/778 is 41/39678.