GCF of 459/920, 408/617
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 459/920, 408/617 i.e 51/567640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 459/920, 408/617.
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 459/920,408/617?
Given fractions are 459/920,408/617
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 459/920,408/617, numerators are 459,408
Denominators are 920,617
The GCF of 459,408 is 51 .
LCM of 920,617 is 567640.
The greatest common factor of 459/920,408/617 = [GCF of 459,408]/[LCM of 920,617]= 51/567640
Therefore, the GCF of 459/920,408/617 is 51/567640.
To find the highest common factor of 459,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 459,408 is 51.
Lets's calculate GCF of 459,408
| 3 | 459, 408 |
| 17 | 153, 136 |
| 9, 8 |
∴ So the GCF of the given numbers is 3 x 17 = 51
Greatest Common Factor of 459,408 By Matching Biggest Common Factor Method
Now, list down the factors of 459
:1,3,9,17,27,51,153,459
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 459,408 . The biggest common factor number is the GCF number.
So the greatest common factor 459,408 is 51.
Lets's calculate LCM of 920,617
Given numbers has no common factors except 1. So, there LCM is their product i.e 567640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 51/567640
Therefore, the GCF of Fractions 459/920,408/617 is 51/567640
Least Common Multiple of 920,617 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 920,617 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(920,617) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(920,617) x common factors =1 x 1 = 1
LCM(920,617) = ( 920 × 617 ) / 1
LCM(920,617) = 567640 / 1
LCM(920,617) = 567640
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FAQs on GCF of Fractions of 459/920, 408/617
1. What is the HCF of 459,408?
The HCF of 459,408 is 51
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 459/920, 408/617?
Answer: GCF of Numerators as per given numbers 459/920, 408/617 is
GCF of Numerators i.e. for 459,408 is 51
LCM of denominators i.e. for 920,617 is 567640.
Thus, GCF of Fractions is 51/567640.Finally, GCF of Fractions for 459/920, 408/617 is 51/567640.