GCF of 30/904, 96/686, 417/676
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/904, 96/686, 417/676 i.e 3/52402168 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/904, 96/686, 417/676.
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 30/904,96/686,417/676?
Given fractions are 30/904,96/686,417/676
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 30/904,96/686,417/676, numerators are 30,96,417
Denominators are 904,686,676
The GCF of 30,96,417 is 3 .
LCM of 904,686,676 is 52402168.
The greatest common factor of 30/904,96/686,417/676 = [GCF of 30,96,417]/[LCM of 904,686,676]= 3/52402168
Therefore, the GCF of 30/904,96/686,417/676 is 3/52402168.
To find the highest common factor of 30,96,417, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 417 are 1, 3, 139, 417
The HCF of 30,96,417 is 3.
Lets's calculate GCF of 30,96,417
| 3 | 30, 96, 417 |
| 10, 32, 139 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 30,96,417 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 417
:1,3,139,417
Greatest Common Factor
We found the factors 30,96,417 . The biggest common factor number is the GCF number.
So the greatest common factor 30,96,417 is 3.
Lets's calculate LCM of 904,686,676
| 2 | 904, 686, 676 |
| 2 | 452, 343, 338 |
| 226, 343, 169 |
∴ So the LCM of the given numbers is 2 x 2 x 226 x 343 x 169 = 52402168
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/52402168
Therefore, the GCF of Fractions 30/904,96/686,417/676 is 3/52402168
Least Common Multiple of 904,686,676 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 904,686,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(904,686,676) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(904,686,676) x common factors =2 x 4 = 8
LCM(904,686,676) = ( 904 × 686 × 676 ) / 8
LCM(904,686,676) = 419217344 / 8
LCM(904,686,676) = 52402168
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 30/904, 96/686, 417/676
1. What is the HCF of 30,96,417?
The HCF of 30,96,417 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 30/904, 96/686, 417/676?
Answer: GCF of Numerators as per given numbers 30/904, 96/686, 417/676 is
GCF of Numerators i.e. for 30,96,417 is 3
LCM of denominators i.e. for 904,686,676 is 52402168.
Thus, GCF of Fractions is 3/52402168.Finally, GCF of Fractions for 30/904, 96/686, 417/676 is 3/52402168.