GCF of 458/57, 345/76, 214/77
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 458/57, 345/76, 214/77 i.e 1/17556 easily. The following is the detailed procedure to determine the greatest common factor of fractions 458/57, 345/76, 214/77.
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 458/57,345/76,214/77?
Given fractions are 458/57,345/76,214/77
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 458/57,345/76,214/77, numerators are 458,345,214
Denominators are 57,76,77
The GCF of 458,345,214 is 1 .
LCM of 57,76,77 is 17556.
The greatest common factor of 458/57,345/76,214/77 = [GCF of 458,345,214]/[LCM of 57,76,77]= 1/17556
Therefore, the GCF of 458/57,345/76,214/77 is 1/17556.
To find the highest common factor of 458,345,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 458 are 1, 2, 229, 458
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345
The factors of 214 are 1, 2, 107, 214
The HCF of 458,345,214 is 1.
Lets's calculate GCF of 458,345,214
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 458,345,214 By Matching Biggest Common Factor Method
Now, list down the factors of 458
:1,2,229,458
Now, list down the factors of 345
:1,3,5,15,23,69,115,345
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 458,345,214 . The biggest common factor number is the GCF number.
So the greatest common factor 458,345,214 is 1.
Lets's calculate LCM of 57,76,77
| 19 | 57, 76, 77 |
| 3, 4, 77 |
∴ So the LCM of the given numbers is 19 x 3 x 4 x 77 = 17556
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17556
Therefore, the GCF of Fractions 458/57,345/76,214/77 is 1/17556
Least Common Multiple of 57,76,77 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 57,76,77 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,76,77) = 1
common factors(in case of two or more numbers have common factors) = 19
GCF(57,76,77) x common factors =1 x 19 = 19
LCM(57,76,77) = ( 57 × 76 × 77 ) / 19
LCM(57,76,77) = 333564 / 19
LCM(57,76,77) = 17556
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FAQs on GCF of Fractions of 458/57, 345/76, 214/77
1. What is the HCF of 458,345,214?
The HCF of 458,345,214 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 458/57, 345/76, 214/77?
Answer: GCF of Numerators as per given numbers 458/57, 345/76, 214/77 is
GCF of Numerators i.e. for 458,345,214 is 1
LCM of denominators i.e. for 57,76,77 is 17556.
Thus, GCF of Fractions is 1/17556.Finally, GCF of Fractions for 458/57, 345/76, 214/77 is 1/17556.