GCF of 9200/857, 6720/7154
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9200/857, 6720/7154 i.e 80/6130978 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9200/857, 6720/7154.
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 9200/857,6720/7154?
Given fractions are 9200/857,6720/7154
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 9200/857,6720/7154, numerators are 9200,6720
Denominators are 857,7154
The GCF of 9200,6720 is 80 .
LCM of 857,7154 is 6130978.
The greatest common factor of 9200/857,6720/7154 = [GCF of 9200,6720]/[LCM of 857,7154]= 80/6130978
Therefore, the GCF of 9200/857,6720/7154 is 80/6130978.
To find the highest common factor of 9200,6720, we have to find the factors of both numbers and list the highest common factor.
The factors of 9200 are 1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 40, 46, 50, 80, 92, 100, 115, 184, 200, 230, 368, 400, 460, 575, 920, 1150, 1840, 2300, 4600, 9200
The factors of 6720 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 192, 210, 224, 240, 280, 320, 336, 420, 448, 480, 560, 672, 840, 960, 1120, 1344, 1680, 2240, 3360, 6720
The HCF of 9200,6720 is 80.
Lets's calculate GCF of 9200,6720
| 2 | 9200, 6720 |
| 2 | 4600, 3360 |
| 2 | 2300, 1680 |
| 2 | 1150, 840 |
| 5 | 575, 420 |
| 115, 84 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 5 = 80
Greatest Common Factor of 9200,6720 By Matching Biggest Common Factor Method
Now, list down the factors of 9200
:1,2,4,5,8,10,16,20,23,25,40,46,50,80,92,100,115,184,200,230,368,400,460,575,920,1150,1840,2300,4600,9200
Now, list down the factors of 6720
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30,32,35,40,42,48,56,60,64,70,80,84,96,105,112,120,140,160,168,192,210,224,240,280,320,336,420,448,480,560,672,840,960,1120,1344,1680,2240,3360,6720
Greatest Common Factor
We found the factors 9200,6720 . The biggest common factor number is the GCF number.
So the greatest common factor 9200,6720 is 80.
Lets's calculate LCM of 857,7154
Given numbers has no common factors except 1. So, there LCM is their product i.e 6130978
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 80/6130978
Therefore, the GCF of Fractions 9200/857,6720/7154 is 80/6130978
Least Common Multiple of 857,7154 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 857,7154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(857,7154) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(857,7154) x common factors =1 x 1 = 1
LCM(857,7154) = ( 857 × 7154 ) / 1
LCM(857,7154) = 6130978 / 1
LCM(857,7154) = 6130978
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FAQs on GCF of Fractions of 9200/857, 6720/7154
1. What is the HCF of 9200,6720?
The HCF of 9200,6720 is 80
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 9200/857, 6720/7154?
Answer: GCF of Numerators as per given numbers 9200/857, 6720/7154 is
GCF of Numerators i.e. for 9200,6720 is 80
LCM of denominators i.e. for 857,7154 is 6130978.
Thus, GCF of Fractions is 80/6130978.Finally, GCF of Fractions for 9200/857, 6720/7154 is 80/6130978.