GCF of 40/820, 53/519, 122/289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/820, 53/519, 122/289 i.e 1/122992620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/820, 53/519, 122/289.
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 40/820,53/519,122/289?
Given fractions are 40/820,53/519,122/289
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 40/820,53/519,122/289, numerators are 40,53,122
Denominators are 820,519,289
The GCF of 40,53,122 is 1 .
LCM of 820,519,289 is 122992620.
The greatest common factor of 40/820,53/519,122/289 = [GCF of 40,53,122]/[LCM of 820,519,289]= 1/122992620
Therefore, the GCF of 40/820,53/519,122/289 is 1/122992620.
To find the highest common factor of 40,53,122, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 53 are 1, 53
The factors of 122 are 1, 2, 61, 122
The HCF of 40,53,122 is 1.
Lets's calculate GCF of 40,53,122
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 40,53,122 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 53
:1,53
Now, list down the factors of 122
:1,2,61,122
Greatest Common Factor
We found the factors 40,53,122 . The biggest common factor number is the GCF number.
So the greatest common factor 40,53,122 is 1.
Lets's calculate LCM of 820,519,289
Given numbers has no common factors except 1. So, there LCM is their product i.e 122992620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/122992620
Therefore, the GCF of Fractions 40/820,53/519,122/289 is 1/122992620
Least Common Multiple of 820,519,289 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 820,519,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(820,519,289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(820,519,289) x common factors =1 x 1 = 1
LCM(820,519,289) = ( 820 × 519 × 289 ) / 1
LCM(820,519,289) = 122992620 / 1
LCM(820,519,289) = 122992620
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FAQs on GCF of Fractions of 40/820, 53/519, 122/289
1. What is the HCF of 40,53,122?
The HCF of 40,53,122 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 40/820, 53/519, 122/289?
Answer: GCF of Numerators as per given numbers 40/820, 53/519, 122/289 is
GCF of Numerators i.e. for 40,53,122 is 1
LCM of denominators i.e. for 820,519,289 is 122992620.
Thus, GCF of Fractions is 1/122992620.Finally, GCF of Fractions for 40/820, 53/519, 122/289 is 1/122992620.