GCF of 5467/804, 7728/1488
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5467/804, 7728/1488 i.e 7/99696 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5467/804, 7728/1488.
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 5467/804,7728/1488?
Given fractions are 5467/804,7728/1488
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 5467/804,7728/1488, numerators are 5467,7728
Denominators are 804,1488
The GCF of 5467,7728 is 7 .
LCM of 804,1488 is 99696.
The greatest common factor of 5467/804,7728/1488 = [GCF of 5467,7728]/[LCM of 804,1488]= 7/99696
Therefore, the GCF of 5467/804,7728/1488 is 7/99696.
To find the highest common factor of 5467,7728, we have to find the factors of both numbers and list the highest common factor.
The factors of 5467 are 1, 7, 11, 71, 77, 497, 781, 5467
The factors of 7728 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864, 7728
The HCF of 5467,7728 is 7.
Lets's calculate GCF of 5467,7728
| 7 | 5467, 7728 |
| 781, 1104 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 5467,7728 By Matching Biggest Common Factor Method
Now, list down the factors of 5467
:1,7,11,71,77,497,781,5467
Now, list down the factors of 7728
:1,2,3,4,6,7,8,12,14,16,21,23,24,28,42,46,48,56,69,84,92,112,138,161,168,184,276,322,336,368,483,552,644,966,1104,1288,1932,2576,3864,7728
Greatest Common Factor
We found the factors 5467,7728 . The biggest common factor number is the GCF number.
So the greatest common factor 5467,7728 is 7.
Lets's calculate LCM of 804,1488
| 2 | 804, 1488 |
| 2 | 402, 744 |
| 3 | 201, 372 |
| 67, 124 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 67 x 124 = 99696
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/99696
Therefore, the GCF of Fractions 5467/804,7728/1488 is 7/99696
Least Common Multiple of 804,1488 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 804,1488 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(804,1488) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(804,1488) x common factors =12 x 1 = 12
LCM(804,1488) = ( 804 × 1488 ) / 12
LCM(804,1488) = 1196352 / 12
LCM(804,1488) = 99696
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FAQs on GCF of Fractions of 5467/804, 7728/1488
1. What is the HCF of 5467,7728?
The HCF of 5467,7728 is 7
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 5467/804, 7728/1488?
Answer: GCF of Numerators as per given numbers 5467/804, 7728/1488 is
GCF of Numerators i.e. for 5467,7728 is 7
LCM of denominators i.e. for 804,1488 is 99696.
Thus, GCF of Fractions is 7/99696.Finally, GCF of Fractions for 5467/804, 7728/1488 is 7/99696.