GCF of 122/56, 142/21, 809/64
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 122/56, 142/21, 809/64 i.e 1/1344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 122/56, 142/21, 809/64.
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 122/56,142/21,809/64?
Given fractions are 122/56,142/21,809/64
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 122/56,142/21,809/64, numerators are 122,142,809
Denominators are 56,21,64
The GCF of 122,142,809 is 1 .
LCM of 56,21,64 is 1344.
The greatest common factor of 122/56,142/21,809/64 = [GCF of 122,142,809]/[LCM of 56,21,64]= 1/1344
Therefore, the GCF of 122/56,142/21,809/64 is 1/1344.
To find the highest common factor of 122,142,809, we have to find the factors of both numbers and list the highest common factor.
The factors of 122 are 1, 2, 61, 122
The factors of 142 are 1, 2, 71, 142
The factors of 809 are 1, 809
The HCF of 122,142,809 is 1.
Lets's calculate GCF of 122,142,809
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 122,142,809 By Matching Biggest Common Factor Method
Now, list down the factors of 122
:1,2,61,122
Now, list down the factors of 142
:1,2,71,142
Now, list down the factors of 809
:1,809
Greatest Common Factor
We found the factors 122,142,809 . The biggest common factor number is the GCF number.
So the greatest common factor 122,142,809 is 1.
Lets's calculate LCM of 56,21,64
| 2 | 56, 21, 64 |
| 2 | 28, 21, 32 |
| 2 | 14, 21, 16 |
| 7 | 7, 21, 8 |
| 1, 3, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 7 x 1 x 3 x 8 = 1344
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1344
Therefore, the GCF of Fractions 122/56,142/21,809/64 is 1/1344
Least Common Multiple of 56,21,64 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 56,21,64 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(56,21,64) = 1
common factors(in case of two or more numbers have common factors) = 56
GCF(56,21,64) x common factors =1 x 56 = 56
LCM(56,21,64) = ( 56 × 21 × 64 ) / 56
LCM(56,21,64) = 75264 / 56
LCM(56,21,64) = 1344
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FAQs on GCF of Fractions of 122/56, 142/21, 809/64
1. What is the HCF of 122,142,809?
The HCF of 122,142,809 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 122/56, 142/21, 809/64?
Answer: GCF of Numerators as per given numbers 122/56, 142/21, 809/64 is
GCF of Numerators i.e. for 122,142,809 is 1
LCM of denominators i.e. for 56,21,64 is 1344.
Thus, GCF of Fractions is 1/1344.Finally, GCF of Fractions for 122/56, 142/21, 809/64 is 1/1344.