GCF of 7680/729, 9131/3402
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7680/729, 9131/3402 i.e 1/10206 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7680/729, 9131/3402.
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 7680/729,9131/3402?
Given fractions are 7680/729,9131/3402
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 7680/729,9131/3402, numerators are 7680,9131
Denominators are 729,3402
The GCF of 7680,9131 is 1 .
LCM of 729,3402 is 10206.
The greatest common factor of 7680/729,9131/3402 = [GCF of 7680,9131]/[LCM of 729,3402]= 1/10206
Therefore, the GCF of 7680/729,9131/3402 is 1/10206.
To find the highest common factor of 7680,9131, we have to find the factors of both numbers and list the highest common factor.
The factors of 7680 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1280, 1536, 1920, 2560, 3840, 7680
The factors of 9131 are 1, 23, 397, 9131
The HCF of 7680,9131 is 1.
Lets's calculate GCF of 7680,9131
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7680,9131 By Matching Biggest Common Factor Method
Now, list down the factors of 7680
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,128,160,192,240,256,320,384,480,512,640,768,960,1280,1536,1920,2560,3840,7680
Now, list down the factors of 9131
:1,23,397,9131
Greatest Common Factor
We found the factors 7680,9131 . The biggest common factor number is the GCF number.
So the greatest common factor 7680,9131 is 1.
Lets's calculate LCM of 729,3402
| 3 | 729, 3402 |
| 3 | 243, 1134 |
| 3 | 81, 378 |
| 3 | 27, 126 |
| 3 | 9, 42 |
| 3, 14 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 3 x 3 x 3 x 14 = 10206
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10206
Therefore, the GCF of Fractions 7680/729,9131/3402 is 1/10206
Least Common Multiple of 729,3402 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 729,3402 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(729,3402) = 243
common factors(in case of two or more numbers have common factors) = 1
GCF(729,3402) x common factors =243 x 1 = 243
LCM(729,3402) = ( 729 × 3402 ) / 243
LCM(729,3402) = 2480058 / 243
LCM(729,3402) = 10206
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FAQs on GCF of Fractions of 7680/729, 9131/3402
1. What is the HCF of 7680,9131?
The HCF of 7680,9131 is 1
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 7680/729, 9131/3402?
Answer: GCF of Numerators as per given numbers 7680/729, 9131/3402 is
GCF of Numerators i.e. for 7680,9131 is 1
LCM of denominators i.e. for 729,3402 is 10206.
Thus, GCF of Fractions is 1/10206.Finally, GCF of Fractions for 7680/729, 9131/3402 is 1/10206.