GCF of 184/30, 472/31, 423/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 184/30, 472/31, 423/21 i.e 1/6510 easily. The following is the detailed procedure to determine the greatest common factor of fractions 184/30, 472/31, 423/21.
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 184/30,472/31,423/21?
Given fractions are 184/30,472/31,423/21
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 184/30,472/31,423/21, numerators are 184,472,423
Denominators are 30,31,21
The GCF of 184,472,423 is 1 .
LCM of 30,31,21 is 6510.
The greatest common factor of 184/30,472/31,423/21 = [GCF of 184,472,423]/[LCM of 30,31,21]= 1/6510
Therefore, the GCF of 184/30,472/31,423/21 is 1/6510.
To find the highest common factor of 184,472,423, we have to find the factors of both numbers and list the highest common factor.
The factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184
The factors of 472 are 1, 2, 4, 8, 59, 118, 236, 472
The factors of 423 are 1, 3, 9, 47, 141, 423
The HCF of 184,472,423 is 1.
Lets's calculate GCF of 184,472,423
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 184,472,423 By Matching Biggest Common Factor Method
Now, list down the factors of 184
:1,2,4,8,23,46,92,184
Now, list down the factors of 472
:1,2,4,8,59,118,236,472
Now, list down the factors of 423
:1,3,9,47,141,423
Greatest Common Factor
We found the factors 184,472,423 . The biggest common factor number is the GCF number.
So the greatest common factor 184,472,423 is 1.
Lets's calculate LCM of 30,31,21
| 3 | 30, 31, 21 |
| 10, 31, 7 |
∴ So the LCM of the given numbers is 3 x 10 x 31 x 7 = 6510
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6510
Therefore, the GCF of Fractions 184/30,472/31,423/21 is 1/6510
Least Common Multiple of 30,31,21 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 30,31,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,31,21) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(30,31,21) x common factors =1 x 3 = 3
LCM(30,31,21) = ( 30 × 31 × 21 ) / 3
LCM(30,31,21) = 19530 / 3
LCM(30,31,21) = 6510
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FAQs on GCF of Fractions of 184/30, 472/31, 423/21
1. What is the HCF of 184,472,423?
The HCF of 184,472,423 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 184/30, 472/31, 423/21?
Answer: GCF of Numerators as per given numbers 184/30, 472/31, 423/21 is
GCF of Numerators i.e. for 184,472,423 is 1
LCM of denominators i.e. for 30,31,21 is 6510.
Thus, GCF of Fractions is 1/6510.Finally, GCF of Fractions for 184/30, 472/31, 423/21 is 1/6510.