GCF of 7920/460, 9405/341
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7920/460, 9405/341 i.e 495/156860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7920/460, 9405/341.
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 7920/460,9405/341?
Given fractions are 7920/460,9405/341
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 7920/460,9405/341, numerators are 7920,9405
Denominators are 460,341
The GCF of 7920,9405 is 495 .
LCM of 460,341 is 156860.
The greatest common factor of 7920/460,9405/341 = [GCF of 7920,9405]/[LCM of 460,341]= 495/156860
Therefore, the GCF of 7920/460,9405/341 is 495/156860.
To find the highest common factor of 7920,9405, we have to find the factors of both numbers and list the highest common factor.
The factors of 7920 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 99, 110, 120, 132, 144, 165, 176, 180, 198, 220, 240, 264, 330, 360, 396, 440, 495, 528, 660, 720, 792, 880, 990, 1320, 1584, 1980, 2640, 3960, 7920
The factors of 9405 are 1, 3, 5, 9, 11, 15, 19, 33, 45, 55, 57, 95, 99, 165, 171, 209, 285, 495, 627, 855, 1045, 1881, 3135, 9405
The HCF of 7920,9405 is 495.
Lets's calculate GCF of 7920,9405
| 3 | 7920, 9405 |
| 3 | 2640, 3135 |
| 5 | 880, 1045 |
| 11 | 176, 209 |
| 16, 19 |
∴ So the GCF of the given numbers is 3 x 3 x 5 x 11 = 495
Greatest Common Factor of 7920,9405 By Matching Biggest Common Factor Method
Now, list down the factors of 7920
:1,2,3,4,5,6,8,9,10,11,12,15,16,18,20,22,24,30,33,36,40,44,45,48,55,60,66,72,80,88,90,99,110,120,132,144,165,176,180,198,220,240,264,330,360,396,440,495,528,660,720,792,880,990,1320,1584,1980,2640,3960,7920
Now, list down the factors of 9405
:1,3,5,9,11,15,19,33,45,55,57,95,99,165,171,209,285,495,627,855,1045,1881,3135,9405
Greatest Common Factor
We found the factors 7920,9405 . The biggest common factor number is the GCF number.
So the greatest common factor 7920,9405 is 495.
Lets's calculate LCM of 460,341
Given numbers has no common factors except 1. So, there LCM is their product i.e 156860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 495/156860
Therefore, the GCF of Fractions 7920/460,9405/341 is 495/156860
Least Common Multiple of 460,341 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 460,341 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(460,341) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(460,341) x common factors =1 x 1 = 1
LCM(460,341) = ( 460 × 341 ) / 1
LCM(460,341) = 156860 / 1
LCM(460,341) = 156860
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FAQs on GCF of Fractions of 7920/460, 9405/341
1. What is the HCF of 7920,9405?
The HCF of 7920,9405 is 495
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 7920/460, 9405/341?
Answer: GCF of Numerators as per given numbers 7920/460, 9405/341 is
GCF of Numerators i.e. for 7920,9405 is 495
LCM of denominators i.e. for 460,341 is 156860.
Thus, GCF of Fractions is 495/156860.Finally, GCF of Fractions for 7920/460, 9405/341 is 495/156860.