GCF of 9100/420, 7805/612
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9100/420, 7805/612 i.e 35/21420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9100/420, 7805/612.
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 9100/420,7805/612?
Given fractions are 9100/420,7805/612
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 9100/420,7805/612, numerators are 9100,7805
Denominators are 420,612
The GCF of 9100,7805 is 35 .
LCM of 420,612 is 21420.
The greatest common factor of 9100/420,7805/612 = [GCF of 9100,7805]/[LCM of 420,612]= 35/21420
Therefore, the GCF of 9100/420,7805/612 is 35/21420.
To find the highest common factor of 9100,7805, we have to find the factors of both numbers and list the highest common factor.
The factors of 9100 are 1, 2, 4, 5, 7, 10, 13, 14, 20, 25, 26, 28, 35, 50, 52, 65, 70, 91, 100, 130, 140, 175, 182, 260, 325, 350, 364, 455, 650, 700, 910, 1300, 1820, 2275, 4550, 9100
The factors of 7805 are 1, 5, 7, 35, 223, 1115, 1561, 7805
The HCF of 9100,7805 is 35.
Lets's calculate GCF of 9100,7805
| 5 | 9100, 7805 |
| 7 | 1820, 1561 |
| 260, 223 |
∴ So the GCF of the given numbers is 5 x 7 = 35
Greatest Common Factor of 9100,7805 By Matching Biggest Common Factor Method
Now, list down the factors of 9100
:1,2,4,5,7,10,13,14,20,25,26,28,35,50,52,65,70,91,100,130,140,175,182,260,325,350,364,455,650,700,910,1300,1820,2275,4550,9100
Now, list down the factors of 7805
:1,5,7,35,223,1115,1561,7805
Greatest Common Factor
We found the factors 9100,7805 . The biggest common factor number is the GCF number.
So the greatest common factor 9100,7805 is 35.
Lets's calculate LCM of 420,612
| 2 | 420, 612 |
| 2 | 210, 306 |
| 3 | 105, 153 |
| 35, 51 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 35 x 51 = 21420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 35/21420
Therefore, the GCF of Fractions 9100/420,7805/612 is 35/21420
Least Common Multiple of 420,612 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 420,612 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,612) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(420,612) x common factors =12 x 1 = 12
LCM(420,612) = ( 420 × 612 ) / 12
LCM(420,612) = 257040 / 12
LCM(420,612) = 21420
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FAQs on GCF of Fractions of 9100/420, 7805/612
1. What is the HCF of 9100,7805?
The HCF of 9100,7805 is 35
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 9100/420, 7805/612?
Answer: GCF of Numerators as per given numbers 9100/420, 7805/612 is
GCF of Numerators i.e. for 9100,7805 is 35
LCM of denominators i.e. for 420,612 is 21420.
Thus, GCF of Fractions is 35/21420.Finally, GCF of Fractions for 9100/420, 7805/612 is 35/21420.