GCF of 584/51, 7314/977
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 584/51, 7314/977 i.e 2/49827 easily. The following is the detailed procedure to determine the greatest common factor of fractions 584/51, 7314/977.
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 584/51,7314/977?
Given fractions are 584/51,7314/977
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 584/51,7314/977, numerators are 584,7314
Denominators are 51,977
The GCF of 584,7314 is 2 .
LCM of 51,977 is 49827.
The greatest common factor of 584/51,7314/977 = [GCF of 584,7314]/[LCM of 51,977]= 2/49827
Therefore, the GCF of 584/51,7314/977 is 2/49827.
To find the highest common factor of 584,7314, 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 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314
The HCF of 584,7314 is 2.
Lets's calculate GCF of 584,7314
| 2 | 584, 7314 |
| 292, 3657 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 584,7314 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 7314
:1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314
Greatest Common Factor
We found the factors 584,7314 . The biggest common factor number is the GCF number.
So the greatest common factor 584,7314 is 2.
Lets's calculate LCM of 51,977
Given numbers has no common factors except 1. So, there LCM is their product i.e 49827
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/49827
Therefore, the GCF of Fractions 584/51,7314/977 is 2/49827
Least Common Multiple of 51,977 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 51,977 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,977) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(51,977) x common factors =1 x 1 = 1
LCM(51,977) = ( 51 × 977 ) / 1
LCM(51,977) = 49827 / 1
LCM(51,977) = 49827
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FAQs on GCF of Fractions of 584/51, 7314/977
1. What is the HCF of 584,7314?
The HCF of 584,7314 is 2
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 584/51, 7314/977?
Answer: GCF of Numerators as per given numbers 584/51, 7314/977 is
GCF of Numerators i.e. for 584,7314 is 2
LCM of denominators i.e. for 51,977 is 49827.
Thus, GCF of Fractions is 2/49827.Finally, GCF of Fractions for 584/51, 7314/977 is 2/49827.