GCF of 7812/304, 8829/9021
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7812/304, 8829/9021 i.e 9/2742384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7812/304, 8829/9021.
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 7812/304,8829/9021?
Given fractions are 7812/304,8829/9021
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 7812/304,8829/9021, numerators are 7812,8829
Denominators are 304,9021
The GCF of 7812,8829 is 9 .
LCM of 304,9021 is 2742384.
The greatest common factor of 7812/304,8829/9021 = [GCF of 7812,8829]/[LCM of 304,9021]= 9/2742384
Therefore, the GCF of 7812/304,8829/9021 is 9/2742384.
To find the highest common factor of 7812,8829, we have to find the factors of both numbers and list the highest common factor.
The factors of 7812 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 31, 36, 42, 62, 63, 84, 93, 124, 126, 186, 217, 252, 279, 372, 434, 558, 651, 868, 1116, 1302, 1953, 2604, 3906, 7812
The factors of 8829 are 1, 3, 9, 27, 81, 109, 327, 981, 2943, 8829
The HCF of 7812,8829 is 9.
Lets's calculate GCF of 7812,8829
| 3 | 7812, 8829 |
| 3 | 2604, 2943 |
| 868, 981 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 7812,8829 By Matching Biggest Common Factor Method
Now, list down the factors of 7812
:1,2,3,4,6,7,9,12,14,18,21,28,31,36,42,62,63,84,93,124,126,186,217,252,279,372,434,558,651,868,1116,1302,1953,2604,3906,7812
Now, list down the factors of 8829
:1,3,9,27,81,109,327,981,2943,8829
Greatest Common Factor
We found the factors 7812,8829 . The biggest common factor number is the GCF number.
So the greatest common factor 7812,8829 is 9.
Lets's calculate LCM of 304,9021
Given numbers has no common factors except 1. So, there LCM is their product i.e 2742384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/2742384
Therefore, the GCF of Fractions 7812/304,8829/9021 is 9/2742384
Least Common Multiple of 304,9021 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 304,9021 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(304,9021) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(304,9021) x common factors =1 x 1 = 1
LCM(304,9021) = ( 304 × 9021 ) / 1
LCM(304,9021) = 2742384 / 1
LCM(304,9021) = 2742384
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FAQs on GCF of Fractions of 7812/304, 8829/9021
1. What is the HCF of 7812,8829?
The HCF of 7812,8829 is 9
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 7812/304, 8829/9021?
Answer: GCF of Numerators as per given numbers 7812/304, 8829/9021 is
GCF of Numerators i.e. for 7812,8829 is 9
LCM of denominators i.e. for 304,9021 is 2742384.
Thus, GCF of Fractions is 9/2742384.Finally, GCF of Fractions for 7812/304, 8829/9021 is 9/2742384.