GCF of 4000/889, 7000/7209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4000/889, 7000/7209 i.e 1000/6408801 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4000/889, 7000/7209.
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 4000/889,7000/7209?
Given fractions are 4000/889,7000/7209
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 4000/889,7000/7209, numerators are 4000,7000
Denominators are 889,7209
The GCF of 4000,7000 is 1000 .
LCM of 889,7209 is 6408801.
The greatest common factor of 4000/889,7000/7209 = [GCF of 4000,7000]/[LCM of 889,7209]= 1000/6408801
Therefore, the GCF of 4000/889,7000/7209 is 1000/6408801.
To find the highest common factor of 4000,7000, we have to find the factors of both numbers and list the highest common factor.
The factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000
The factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000
The HCF of 4000,7000 is 1000.
Lets's calculate GCF of 4000,7000
| 2 | 4000, 7000 |
| 2 | 2000, 3500 |
| 2 | 1000, 1750 |
| 5 | 500, 875 |
| 5 | 100, 175 |
| 5 | 20, 35 |
| 4, 7 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 x 5 x 5 = 1000
Greatest Common Factor of 4000,7000 By Matching Biggest Common Factor Method
Now, list down the factors of 4000
:1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,500,800,1000,2000,4000
Now, list down the factors of 7000
:1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,125,140,175,200,250,280,350,500,700,875,1000,1400,1750,3500,7000
Greatest Common Factor
We found the factors 4000,7000 . The biggest common factor number is the GCF number.
So the greatest common factor 4000,7000 is 1000.
Lets's calculate LCM of 889,7209
Given numbers has no common factors except 1. So, there LCM is their product i.e 6408801
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1000/6408801
Therefore, the GCF of Fractions 4000/889,7000/7209 is 1000/6408801
Least Common Multiple of 889,7209 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 889,7209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(889,7209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(889,7209) x common factors =1 x 1 = 1
LCM(889,7209) = ( 889 × 7209 ) / 1
LCM(889,7209) = 6408801 / 1
LCM(889,7209) = 6408801
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FAQs on GCF of Fractions of 4000/889, 7000/7209
1. What is the HCF of 4000,7000?
The HCF of 4000,7000 is 1000
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 4000/889, 7000/7209?
Answer: GCF of Numerators as per given numbers 4000/889, 7000/7209 is
GCF of Numerators i.e. for 4000,7000 is 1000
LCM of denominators i.e. for 889,7209 is 6408801.
Thus, GCF of Fractions is 1000/6408801.Finally, GCF of Fractions for 4000/889, 7000/7209 is 1000/6408801.