GCF of 413/30, 767/9549
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 413/30, 767/9549 i.e 59/95490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 413/30, 767/9549.
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 413/30,767/9549?
Given fractions are 413/30,767/9549
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 413/30,767/9549, numerators are 413,767
Denominators are 30,9549
The GCF of 413,767 is 59 .
LCM of 30,9549 is 95490.
The greatest common factor of 413/30,767/9549 = [GCF of 413,767]/[LCM of 30,9549]= 59/95490
Therefore, the GCF of 413/30,767/9549 is 59/95490.
To find the highest common factor of 413,767, 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 767 are 1, 13, 59, 767
The HCF of 413,767 is 59.
Lets's calculate GCF of 413,767
| 59 | 413, 767 |
| 7, 13 |
∴ So the GCF of the given numbers is 59 = 59
Greatest Common Factor of 413,767 By Matching Biggest Common Factor Method
Now, list down the factors of 413
:1,7,59,413
Now, list down the factors of 767
:1,13,59,767
Greatest Common Factor
We found the factors 413,767 . The biggest common factor number is the GCF number.
So the greatest common factor 413,767 is 59.
Lets's calculate LCM of 30,9549
| 3 | 30, 9549 |
| 10, 3183 |
∴ So the LCM of the given numbers is 3 x 10 x 3183 = 95490
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 59/95490
Therefore, the GCF of Fractions 413/30,767/9549 is 59/95490
Least Common Multiple of 30,9549 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 30,9549 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,9549) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(30,9549) x common factors =3 x 1 = 3
LCM(30,9549) = ( 30 × 9549 ) / 3
LCM(30,9549) = 286470 / 3
LCM(30,9549) = 95490
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FAQs on GCF of Fractions of 413/30, 767/9549
1. What is the HCF of 413,767?
The HCF of 413,767 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 413/30, 767/9549?
Answer: GCF of Numerators as per given numbers 413/30, 767/9549 is
GCF of Numerators i.e. for 413,767 is 59
LCM of denominators i.e. for 30,9549 is 95490.
Thus, GCF of Fractions is 59/95490.Finally, GCF of Fractions for 413/30, 767/9549 is 59/95490.