GCF of 82/25, 76/45, 34/57, 22/408
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/25, 76/45, 34/57, 22/408 i.e 2/581400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/25, 76/45, 34/57, 22/408.
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 82/25,76/45,34/57,22/408?
Given fractions are 82/25,76/45,34/57,22/408
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 82/25,76/45,34/57,22/408, numerators are 82,76,34,22
Denominators are 25,45,57,408
The GCF of 82,76,34,22 is 2 .
LCM of 25,45,57,408 is 581400.
The greatest common factor of 82/25,76/45,34/57,22/408 = [GCF of 82,76,34,22]/[LCM of 25,45,57,408]= 2/581400
Therefore, the GCF of 82/25,76/45,34/57,22/408 is 2/581400.
To find the highest common factor of 82,76,34,22, 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 76 are 1, 2, 4, 19, 38, 76
The factors of 34 are 1, 2, 17, 34
The factors of 22 are 1, 2, 11, 22
The HCF of 82,76,34,22 is 2.
Lets's calculate GCF of 82,76,34,22
| 2 | 82, 76, 34, 22 |
| 41, 38, 17, 11 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 82,76,34,22 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 22
:1,2,11,22
Greatest Common Factor
We found the factors 82,76,34,22 . The biggest common factor number is the GCF number.
So the greatest common factor 82,76,34,22 is 2.
Lets's calculate LCM of 25,45,57,408
| 3 | 25, 45, 57, 408 |
| 5 | 25, 15, 19, 136 |
| 5, 3, 19, 136 |
∴ So the LCM of the given numbers is 3 x 5 x 5 x 3 x 19 x 136 = 581400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/581400
Therefore, the GCF of Fractions 82/25,76/45,34/57,22/408 is 2/581400
Least Common Multiple of 25,45,57,408 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 25,45,57,408 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(25,45,57,408) = 1
common factors(in case of two or more numbers have common factors) = 45
GCF(25,45,57,408) x common factors =1 x 45 = 45
LCM(25,45,57,408) = ( 25 × 45 × 57 × 408 ) / 45
LCM(25,45,57,408) = 26163000 / 45
LCM(25,45,57,408) = 581400
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 82/25, 76/45, 34/57, 22/408
1. What is the HCF of 82,76,34,22?
The HCF of 82,76,34,22 is 2
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 82/25, 76/45, 34/57, 22/408?
Answer: GCF of Numerators as per given numbers 82/25, 76/45, 34/57, 22/408 is
GCF of Numerators i.e. for 82,76,34,22 is 2
LCM of denominators i.e. for 25,45,57,408 is 581400.
Thus, GCF of Fractions is 2/581400.Finally, GCF of Fractions for 82/25, 76/45, 34/57, 22/408 is 2/581400.