GCF of 4514/463, 8784/1027
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4514/463, 8784/1027 i.e 122/475501 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4514/463, 8784/1027.
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 4514/463,8784/1027?
Given fractions are 4514/463,8784/1027
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 4514/463,8784/1027, numerators are 4514,8784
Denominators are 463,1027
The GCF of 4514,8784 is 122 .
LCM of 463,1027 is 475501.
The greatest common factor of 4514/463,8784/1027 = [GCF of 4514,8784]/[LCM of 463,1027]= 122/475501
Therefore, the GCF of 4514/463,8784/1027 is 122/475501.
To find the highest common factor of 4514,8784, we have to find the factors of both numbers and list the highest common factor.
The factors of 4514 are 1, 2, 37, 61, 74, 122, 2257, 4514
The factors of 8784 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 61, 72, 122, 144, 183, 244, 366, 488, 549, 732, 976, 1098, 1464, 2196, 2928, 4392, 8784
The HCF of 4514,8784 is 122.
Lets's calculate GCF of 4514,8784
| 2 | 4514, 8784 |
| 61 | 2257, 4392 |
| 37, 72 |
∴ So the GCF of the given numbers is 2 x 61 = 122
Greatest Common Factor of 4514,8784 By Matching Biggest Common Factor Method
Now, list down the factors of 4514
:1,2,37,61,74,122,2257,4514
Now, list down the factors of 8784
:1,2,3,4,6,8,9,12,16,18,24,36,48,61,72,122,144,183,244,366,488,549,732,976,1098,1464,2196,2928,4392,8784
Greatest Common Factor
We found the factors 4514,8784 . The biggest common factor number is the GCF number.
So the greatest common factor 4514,8784 is 122.
Lets's calculate LCM of 463,1027
Given numbers has no common factors except 1. So, there LCM is their product i.e 475501
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 122/475501
Therefore, the GCF of Fractions 4514/463,8784/1027 is 122/475501
Least Common Multiple of 463,1027 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 463,1027 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(463,1027) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(463,1027) x common factors =1 x 1 = 1
LCM(463,1027) = ( 463 × 1027 ) / 1
LCM(463,1027) = 475501 / 1
LCM(463,1027) = 475501
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FAQs on GCF of Fractions of 4514/463, 8784/1027
1. What is the HCF of 4514,8784?
The HCF of 4514,8784 is 122
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 4514/463, 8784/1027?
Answer: GCF of Numerators as per given numbers 4514/463, 8784/1027 is
GCF of Numerators i.e. for 4514,8784 is 122
LCM of denominators i.e. for 463,1027 is 475501.
Thus, GCF of Fractions is 122/475501.Finally, GCF of Fractions for 4514/463, 8784/1027 is 122/475501.