GCF of 413/418, 590/642
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 413/418, 590/642 i.e 59/134178 easily. The following is the detailed procedure to determine the greatest common factor of fractions 413/418, 590/642.
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 413/418,590/642?
Given fractions are 413/418,590/642
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 413/418,590/642, numerators are 413,590
Denominators are 418,642
The GCF of 413,590 is 59 .
LCM of 418,642 is 134178.
The greatest common factor of 413/418,590/642 = [GCF of 413,590]/[LCM of 418,642]= 59/134178
Therefore, the GCF of 413/418,590/642 is 59/134178.
To find the highest common factor of 413,590, we have to find the factors of both numbers and list the highest common factor.
The factors of 413 are 1, 7, 59, 413
The factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590
The HCF of 413,590 is 59.
Lets's calculate GCF of 413,590
| 59 | 413, 590 |
| 7, 10 |
∴ So the GCF of the given numbers is 59 = 59
Greatest Common Factor of 413,590 By Matching Biggest Common Factor Method
Now, list down the factors of 413
:1,7,59,413
Now, list down the factors of 590
:1,2,5,10,59,118,295,590
Greatest Common Factor
We found the factors 413,590 . The biggest common factor number is the GCF number.
So the greatest common factor 413,590 is 59.
Lets's calculate LCM of 418,642
| 2 | 418, 642 |
| 209, 321 |
∴ So the LCM of the given numbers is 2 x 209 x 321 = 134178
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 59/134178
Therefore, the GCF of Fractions 413/418,590/642 is 59/134178
Least Common Multiple of 418,642 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 418,642 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(418,642) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(418,642) x common factors =2 x 1 = 2
LCM(418,642) = ( 418 × 642 ) / 2
LCM(418,642) = 268356 / 2
LCM(418,642) = 134178
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FAQs on GCF of Fractions of 413/418, 590/642
1. What is the HCF of 413,590?
The HCF of 413,590 is 59
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 413/418, 590/642?
Answer: GCF of Numerators as per given numbers 413/418, 590/642 is
GCF of Numerators i.e. for 413,590 is 59
LCM of denominators i.e. for 418,642 is 134178.
Thus, GCF of Fractions is 59/134178.Finally, GCF of Fractions for 413/418, 590/642 is 59/134178.