GCF of 189/71, 762/29, 417/16
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 189/71, 762/29, 417/16 i.e 3/32944 easily. The following is the detailed procedure to determine the greatest common factor of fractions 189/71, 762/29, 417/16.
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 189/71,762/29,417/16?
Given fractions are 189/71,762/29,417/16
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 189/71,762/29,417/16, numerators are 189,762,417
Denominators are 71,29,16
The GCF of 189,762,417 is 3 .
LCM of 71,29,16 is 32944.
The greatest common factor of 189/71,762/29,417/16 = [GCF of 189,762,417]/[LCM of 71,29,16]= 3/32944
Therefore, the GCF of 189/71,762/29,417/16 is 3/32944.
To find the highest common factor of 189,762,417, we have to find the factors of both numbers and list the highest common factor.
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The factors of 417 are 1, 3, 139, 417
The HCF of 189,762,417 is 3.
Lets's calculate GCF of 189,762,417
| 3 | 189, 762, 417 |
| 63, 254, 139 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 189,762,417 By Matching Biggest Common Factor Method
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Now, list down the factors of 417
:1,3,139,417
Greatest Common Factor
We found the factors 189,762,417 . The biggest common factor number is the GCF number.
So the greatest common factor 189,762,417 is 3.
Lets's calculate LCM of 71,29,16
Given numbers has no common factors except 1. So, there LCM is their product i.e 32944
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/32944
Therefore, the GCF of Fractions 189/71,762/29,417/16 is 3/32944
Least Common Multiple of 71,29,16 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 71,29,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,29,16) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,29,16) x common factors =1 x 1 = 1
LCM(71,29,16) = ( 71 × 29 × 16 ) / 1
LCM(71,29,16) = 32944 / 1
LCM(71,29,16) = 32944
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FAQs on GCF of Fractions of 189/71, 762/29, 417/16
1. What is the HCF of 189,762,417?
The HCF of 189,762,417 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 189/71, 762/29, 417/16?
Answer: GCF of Numerators as per given numbers 189/71, 762/29, 417/16 is
GCF of Numerators i.e. for 189,762,417 is 3
LCM of denominators i.e. for 71,29,16 is 32944.
Thus, GCF of Fractions is 3/32944.Finally, GCF of Fractions for 189/71, 762/29, 417/16 is 3/32944.