GCF of 21/42, 61/77, 81/512
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 21/42, 61/77, 81/512 i.e 1/118272 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/42, 61/77, 81/512.
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 21/42,61/77,81/512?
Given fractions are 21/42,61/77,81/512
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 21/42,61/77,81/512, numerators are 21,61,81
Denominators are 42,77,512
The GCF of 21,61,81 is 1 .
LCM of 42,77,512 is 118272.
The greatest common factor of 21/42,61/77,81/512 = [GCF of 21,61,81]/[LCM of 42,77,512]= 1/118272
Therefore, the GCF of 21/42,61/77,81/512 is 1/118272.
To find the highest common factor of 21,61,81, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 61 are 1, 61
The factors of 81 are 1, 3, 9, 27, 81
The HCF of 21,61,81 is 1.
Lets's calculate GCF of 21,61,81
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 21,61,81 By Matching Biggest Common Factor Method
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 61
:1,61
Now, list down the factors of 81
:1,3,9,27,81
Greatest Common Factor
We found the factors 21,61,81 . The biggest common factor number is the GCF number.
So the greatest common factor 21,61,81 is 1.
Lets's calculate LCM of 42,77,512
| 2 | 42, 77, 512 |
| 7 | 21, 77, 256 |
| 3, 11, 256 |
∴ So the LCM of the given numbers is 2 x 7 x 3 x 11 x 256 = 118272
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/118272
Therefore, the GCF of Fractions 21/42,61/77,81/512 is 1/118272
Least Common Multiple of 42,77,512 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 42,77,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,77,512) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(42,77,512) x common factors =1 x 14 = 14
LCM(42,77,512) = ( 42 × 77 × 512 ) / 14
LCM(42,77,512) = 1655808 / 14
LCM(42,77,512) = 118272
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 21/42, 61/77, 81/512
1. What is the HCF of 21,61,81?
The HCF of 21,61,81 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 21/42, 61/77, 81/512?
Answer: GCF of Numerators as per given numbers 21/42, 61/77, 81/512 is
GCF of Numerators i.e. for 21,61,81 is 1
LCM of denominators i.e. for 42,77,512 is 118272.
Thus, GCF of Fractions is 1/118272.Finally, GCF of Fractions for 21/42, 61/77, 81/512 is 1/118272.