GCF of 72/186, 189/470, 240/861
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 72/186, 189/470, 240/861 i.e 3/12544770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/186, 189/470, 240/861.
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 72/186,189/470,240/861?
Given fractions are 72/186,189/470,240/861
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 72/186,189/470,240/861, numerators are 72,189,240
Denominators are 186,470,861
The GCF of 72,189,240 is 3 .
LCM of 186,470,861 is 12544770.
The greatest common factor of 72/186,189/470,240/861 = [GCF of 72,189,240]/[LCM of 186,470,861]= 3/12544770
Therefore, the GCF of 72/186,189/470,240/861 is 3/12544770.
To find the highest common factor of 72,189,240, we have to find the factors of both numbers and list the highest common factor.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
The HCF of 72,189,240 is 3.
Lets's calculate GCF of 72,189,240
| 3 | 72, 189, 240 |
| 24, 63, 80 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 72,189,240 By Matching Biggest Common Factor Method
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Now, list down the factors of 240
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240
Greatest Common Factor
We found the factors 72,189,240 . The biggest common factor number is the GCF number.
So the greatest common factor 72,189,240 is 3.
Lets's calculate LCM of 186,470,861
| 2 | 186, 470, 861 |
| 3 | 93, 235, 861 |
| 31, 235, 287 |
∴ So the LCM of the given numbers is 2 x 3 x 31 x 235 x 287 = 12544770
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/12544770
Therefore, the GCF of Fractions 72/186,189/470,240/861 is 3/12544770
Least Common Multiple of 186,470,861 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 186,470,861 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(186,470,861) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(186,470,861) x common factors =1 x 6 = 6
LCM(186,470,861) = ( 186 × 470 × 861 ) / 6
LCM(186,470,861) = 75268620 / 6
LCM(186,470,861) = 12544770
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FAQs on GCF of Fractions of 72/186, 189/470, 240/861
1. What is the HCF of 72,189,240?
The HCF of 72,189,240 is 3
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 72/186, 189/470, 240/861?
Answer: GCF of Numerators as per given numbers 72/186, 189/470, 240/861 is
GCF of Numerators i.e. for 72,189,240 is 3
LCM of denominators i.e. for 186,470,861 is 12544770.
Thus, GCF of Fractions is 3/12544770.Finally, GCF of Fractions for 72/186, 189/470, 240/861 is 3/12544770.