GCF of 17/120, 20/867, 266/200
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 17/120, 20/867, 266/200 i.e 1/173400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/120, 20/867, 266/200.
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 17/120,20/867,266/200?
Given fractions are 17/120,20/867,266/200
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 17/120,20/867,266/200, numerators are 17,20,266
Denominators are 120,867,200
The GCF of 17,20,266 is 1 .
LCM of 120,867,200 is 173400.
The greatest common factor of 17/120,20/867,266/200 = [GCF of 17,20,266]/[LCM of 120,867,200]= 1/173400
Therefore, the GCF of 17/120,20/867,266/200 is 1/173400.
To find the highest common factor of 17,20,266, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266
The HCF of 17,20,266 is 1.
Lets's calculate GCF of 17,20,266
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 17,20,266 By Matching Biggest Common Factor Method
Now, list down the factors of 17
:1,17
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 266
:1,2,7,14,19,38,133,266
Greatest Common Factor
We found the factors 17,20,266 . The biggest common factor number is the GCF number.
So the greatest common factor 17,20,266 is 1.
Lets's calculate LCM of 120,867,200
| 2 | 120, 867, 200 |
| 2 | 60, 867, 100 |
| 2 | 30, 867, 50 |
| 3 | 15, 867, 25 |
| 5 | 5, 289, 25 |
| 1, 289, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 1 x 289 x 5 = 173400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/173400
Therefore, the GCF of Fractions 17/120,20/867,266/200 is 1/173400
Least Common Multiple of 120,867,200 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 120,867,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(120,867,200) = 1
common factors(in case of two or more numbers have common factors) = 120
GCF(120,867,200) x common factors =1 x 120 = 120
LCM(120,867,200) = ( 120 × 867 × 200 ) / 120
LCM(120,867,200) = 20808000 / 120
LCM(120,867,200) = 173400
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 17/120, 20/867, 266/200
1. What is the HCF of 17,20,266?
The HCF of 17,20,266 is 1
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 17/120, 20/867, 266/200?
Answer: GCF of Numerators as per given numbers 17/120, 20/867, 266/200 is
GCF of Numerators i.e. for 17,20,266 is 1
LCM of denominators i.e. for 120,867,200 is 173400.
Thus, GCF of Fractions is 1/173400.Finally, GCF of Fractions for 17/120, 20/867, 266/200 is 1/173400.