GCF of 670/540, 419/458
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 670/540, 419/458 i.e 1/123660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 670/540, 419/458.
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 670/540,419/458?
Given fractions are 670/540,419/458
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 670/540,419/458, numerators are 670,419
Denominators are 540,458
The GCF of 670,419 is 1 .
LCM of 540,458 is 123660.
The greatest common factor of 670/540,419/458 = [GCF of 670,419]/[LCM of 540,458]= 1/123660
Therefore, the GCF of 670/540,419/458 is 1/123660.
To find the highest common factor of 670,419, we have to find the factors of both numbers and list the highest common factor.
The factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670
The factors of 419 are 1, 419
The HCF of 670,419 is 1.
Lets's calculate GCF of 670,419
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 670,419 By Matching Biggest Common Factor Method
Now, list down the factors of 670
:1,2,5,10,67,134,335,670
Now, list down the factors of 419
:1,419
Greatest Common Factor
We found the factors 670,419 . The biggest common factor number is the GCF number.
So the greatest common factor 670,419 is 1.
Lets's calculate LCM of 540,458
| 2 | 540, 458 |
| 270, 229 |
∴ So the LCM of the given numbers is 2 x 270 x 229 = 123660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/123660
Therefore, the GCF of Fractions 670/540,419/458 is 1/123660
Least Common Multiple of 540,458 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 540,458 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,458) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(540,458) x common factors =2 x 1 = 2
LCM(540,458) = ( 540 × 458 ) / 2
LCM(540,458) = 247320 / 2
LCM(540,458) = 123660
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FAQs on GCF of Fractions of 670/540, 419/458
1. What is the HCF of 670,419?
The HCF of 670,419 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 670/540, 419/458?
Answer: GCF of Numerators as per given numbers 670/540, 419/458 is
GCF of Numerators i.e. for 670,419 is 1
LCM of denominators i.e. for 540,458 is 123660.
Thus, GCF of Fractions is 1/123660.Finally, GCF of Fractions for 670/540, 419/458 is 1/123660.