GCF of 584/67, 468/1656
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 584/67, 468/1656 i.e 4/110952 easily. The following is the detailed procedure to determine the greatest common factor of fractions 584/67, 468/1656.
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 584/67,468/1656?
Given fractions are 584/67,468/1656
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 584/67,468/1656, numerators are 584,468
Denominators are 67,1656
The GCF of 584,468 is 4 .
LCM of 67,1656 is 110952.
The greatest common factor of 584/67,468/1656 = [GCF of 584,468]/[LCM of 67,1656]= 4/110952
Therefore, the GCF of 584/67,468/1656 is 4/110952.
To find the highest common factor of 584,468, we have to find the factors of both numbers and list the highest common factor.
The factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
The HCF of 584,468 is 4.
Lets's calculate GCF of 584,468
| 2 | 584, 468 |
| 2 | 292, 234 |
| 146, 117 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 584,468 By Matching Biggest Common Factor Method
Now, list down the factors of 584
:1,2,4,8,73,146,292,584
Now, list down the factors of 468
:1,2,3,4,6,9,12,13,18,26,36,39,52,78,117,156,234,468
Greatest Common Factor
We found the factors 584,468 . The biggest common factor number is the GCF number.
So the greatest common factor 584,468 is 4.
Lets's calculate LCM of 67,1656
Given numbers has no common factors except 1. So, there LCM is their product i.e 110952
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/110952
Therefore, the GCF of Fractions 584/67,468/1656 is 4/110952
Least Common Multiple of 67,1656 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 67,1656 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,1656) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(67,1656) x common factors =1 x 1 = 1
LCM(67,1656) = ( 67 × 1656 ) / 1
LCM(67,1656) = 110952 / 1
LCM(67,1656) = 110952
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FAQs on GCF of Fractions of 584/67, 468/1656
1. What is the HCF of 584,468?
The HCF of 584,468 is 4
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 584/67, 468/1656?
Answer: GCF of Numerators as per given numbers 584/67, 468/1656 is
GCF of Numerators i.e. for 584,468 is 4
LCM of denominators i.e. for 67,1656 is 110952.
Thus, GCF of Fractions is 4/110952.Finally, GCF of Fractions for 584/67, 468/1656 is 4/110952.