GCF of 9984/217, 8049/1461
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9984/217, 8049/1461 i.e 3/317037 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9984/217, 8049/1461.
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 9984/217,8049/1461?
Given fractions are 9984/217,8049/1461
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 9984/217,8049/1461, numerators are 9984,8049
Denominators are 217,1461
The GCF of 9984,8049 is 3 .
LCM of 217,1461 is 317037.
The greatest common factor of 9984/217,8049/1461 = [GCF of 9984,8049]/[LCM of 217,1461]= 3/317037
Therefore, the GCF of 9984/217,8049/1461 is 3/317037.
To find the highest common factor of 9984,8049, we have to find the factors of both numbers and list the highest common factor.
The factors of 9984 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 624, 768, 832, 1248, 1664, 2496, 3328, 4992, 9984
The factors of 8049 are 1, 3, 2683, 8049
The HCF of 9984,8049 is 3.
Lets's calculate GCF of 9984,8049
| 3 | 9984, 8049 |
| 3328, 2683 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 9984,8049 By Matching Biggest Common Factor Method
Now, list down the factors of 9984
:1,2,3,4,6,8,12,13,16,24,26,32,39,48,52,64,78,96,104,128,156,192,208,256,312,384,416,624,768,832,1248,1664,2496,3328,4992,9984
Now, list down the factors of 8049
:1,3,2683,8049
Greatest Common Factor
We found the factors 9984,8049 . The biggest common factor number is the GCF number.
So the greatest common factor 9984,8049 is 3.
Lets's calculate LCM of 217,1461
Given numbers has no common factors except 1. So, there LCM is their product i.e 317037
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/317037
Therefore, the GCF of Fractions 9984/217,8049/1461 is 3/317037
Least Common Multiple of 217,1461 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 217,1461 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,1461) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(217,1461) x common factors =1 x 1 = 1
LCM(217,1461) = ( 217 × 1461 ) / 1
LCM(217,1461) = 317037 / 1
LCM(217,1461) = 317037
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FAQs on GCF of Fractions of 9984/217, 8049/1461
1. What is the HCF of 9984,8049?
The HCF of 9984,8049 is 3
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 9984/217, 8049/1461?
Answer: GCF of Numerators as per given numbers 9984/217, 8049/1461 is
GCF of Numerators i.e. for 9984,8049 is 3
LCM of denominators i.e. for 217,1461 is 317037.
Thus, GCF of Fractions is 3/317037.Finally, GCF of Fractions for 9984/217, 8049/1461 is 3/317037.