GCF of 1060/213, 2000/222
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1060/213, 2000/222 i.e 20/15762 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1060/213, 2000/222.
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 1060/213,2000/222?
Given fractions are 1060/213,2000/222
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 1060/213,2000/222, numerators are 1060,2000
Denominators are 213,222
The GCF of 1060,2000 is 20 .
LCM of 213,222 is 15762.
The greatest common factor of 1060/213,2000/222 = [GCF of 1060,2000]/[LCM of 213,222]= 20/15762
Therefore, the GCF of 1060/213,2000/222 is 20/15762.
To find the highest common factor of 1060,2000, we have to find the factors of both numbers and list the highest common factor.
The factors of 1060 are 1, 2, 4, 5, 10, 20, 53, 106, 212, 265, 530, 1060
The factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000
The HCF of 1060,2000 is 20.
Lets's calculate GCF of 1060,2000
| 2 | 1060, 2000 |
| 2 | 530, 1000 |
| 5 | 265, 500 |
| 53, 100 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 1060,2000 By Matching Biggest Common Factor Method
Now, list down the factors of 1060
:1,2,4,5,10,20,53,106,212,265,530,1060
Now, list down the factors of 2000
:1,2,4,5,8,10,16,20,25,40,50,80,100,125,200,250,400,500,1000,2000
Greatest Common Factor
We found the factors 1060,2000 . The biggest common factor number is the GCF number.
So the greatest common factor 1060,2000 is 20.
Lets's calculate LCM of 213,222
| 3 | 213, 222 |
| 71, 74 |
∴ So the LCM of the given numbers is 3 x 71 x 74 = 15762
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/15762
Therefore, the GCF of Fractions 1060/213,2000/222 is 20/15762
Least Common Multiple of 213,222 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 213,222 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(213,222) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(213,222) x common factors =3 x 1 = 3
LCM(213,222) = ( 213 × 222 ) / 3
LCM(213,222) = 47286 / 3
LCM(213,222) = 15762
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1060/213, 2000/222
1. What is the HCF of 1060,2000?
The HCF of 1060,2000 is 20
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 1060/213, 2000/222?
Answer: GCF of Numerators as per given numbers 1060/213, 2000/222 is
GCF of Numerators i.e. for 1060,2000 is 20
LCM of denominators i.e. for 213,222 is 15762.
Thus, GCF of Fractions is 20/15762.Finally, GCF of Fractions for 1060/213, 2000/222 is 20/15762.