GCF of 5380/219, 8784/1953
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5380/219, 8784/1953 i.e 4/142569 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5380/219, 8784/1953.
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 5380/219,8784/1953?
Given fractions are 5380/219,8784/1953
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 5380/219,8784/1953, numerators are 5380,8784
Denominators are 219,1953
The GCF of 5380,8784 is 4 .
LCM of 219,1953 is 142569.
The greatest common factor of 5380/219,8784/1953 = [GCF of 5380,8784]/[LCM of 219,1953]= 4/142569
Therefore, the GCF of 5380/219,8784/1953 is 4/142569.
To find the highest common factor of 5380,8784, we have to find the factors of both numbers and list the highest common factor.
The factors of 5380 are 1, 2, 4, 5, 10, 20, 269, 538, 1076, 1345, 2690, 5380
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 5380,8784 is 4.
Lets's calculate GCF of 5380,8784
| 2 | 5380, 8784 |
| 2 | 2690, 4392 |
| 1345, 2196 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 5380,8784 By Matching Biggest Common Factor Method
Now, list down the factors of 5380
:1,2,4,5,10,20,269,538,1076,1345,2690,5380
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 5380,8784 . The biggest common factor number is the GCF number.
So the greatest common factor 5380,8784 is 4.
Lets's calculate LCM of 219,1953
| 3 | 219, 1953 |
| 73, 651 |
∴ So the LCM of the given numbers is 3 x 73 x 651 = 142569
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/142569
Therefore, the GCF of Fractions 5380/219,8784/1953 is 4/142569
Least Common Multiple of 219,1953 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 219,1953 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,1953) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(219,1953) x common factors =3 x 1 = 3
LCM(219,1953) = ( 219 × 1953 ) / 3
LCM(219,1953) = 427707 / 3
LCM(219,1953) = 142569
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FAQs on GCF of Fractions of 5380/219, 8784/1953
1. What is the HCF of 5380,8784?
The HCF of 5380,8784 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 5380/219, 8784/1953?
Answer: GCF of Numerators as per given numbers 5380/219, 8784/1953 is
GCF of Numerators i.e. for 5380,8784 is 4
LCM of denominators i.e. for 219,1953 is 142569.
Thus, GCF of Fractions is 4/142569.Finally, GCF of Fractions for 5380/219, 8784/1953 is 4/142569.