GCF of 9840/41, 3150/715
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9840/41, 3150/715 i.e 30/29315 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9840/41, 3150/715.
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 9840/41,3150/715?
Given fractions are 9840/41,3150/715
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 9840/41,3150/715, numerators are 9840,3150
Denominators are 41,715
The GCF of 9840,3150 is 30 .
LCM of 41,715 is 29315.
The greatest common factor of 9840/41,3150/715 = [GCF of 9840,3150]/[LCM of 41,715]= 30/29315
Therefore, the GCF of 9840/41,3150/715 is 30/29315.
To find the highest common factor of 9840,3150, we have to find the factors of both numbers and list the highest common factor.
The factors of 9840 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 41, 48, 60, 80, 82, 120, 123, 164, 205, 240, 246, 328, 410, 492, 615, 656, 820, 984, 1230, 1640, 1968, 2460, 3280, 4920, 9840
The factors of 3150 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 30, 35, 42, 45, 50, 63, 70, 75, 90, 105, 126, 150, 175, 210, 225, 315, 350, 450, 525, 630, 1050, 1575, 3150
The HCF of 9840,3150 is 30.
Lets's calculate GCF of 9840,3150
| 2 | 9840, 3150 |
| 3 | 4920, 1575 |
| 5 | 1640, 525 |
| 328, 105 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 9840,3150 By Matching Biggest Common Factor Method
Now, list down the factors of 9840
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,41,48,60,80,82,120,123,164,205,240,246,328,410,492,615,656,820,984,1230,1640,1968,2460,3280,4920,9840
Now, list down the factors of 3150
:1,2,3,5,6,7,9,10,14,15,18,21,25,30,35,42,45,50,63,70,75,90,105,126,150,175,210,225,315,350,450,525,630,1050,1575,3150
Greatest Common Factor
We found the factors 9840,3150 . The biggest common factor number is the GCF number.
So the greatest common factor 9840,3150 is 30.
Lets's calculate LCM of 41,715
Given numbers has no common factors except 1. So, there LCM is their product i.e 29315
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/29315
Therefore, the GCF of Fractions 9840/41,3150/715 is 30/29315
Least Common Multiple of 41,715 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 41,715 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(41,715) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(41,715) x common factors =1 x 1 = 1
LCM(41,715) = ( 41 × 715 ) / 1
LCM(41,715) = 29315 / 1
LCM(41,715) = 29315
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FAQs on GCF of Fractions of 9840/41, 3150/715
1. What is the HCF of 9840,3150?
The HCF of 9840,3150 is 30
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 9840/41, 3150/715?
Answer: GCF of Numerators as per given numbers 9840/41, 3150/715 is
GCF of Numerators i.e. for 9840,3150 is 30
LCM of denominators i.e. for 41,715 is 29315.
Thus, GCF of Fractions is 30/29315.Finally, GCF of Fractions for 9840/41, 3150/715 is 30/29315.