GCF of 444/74, 2184/178
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 444/74, 2184/178 i.e 12/6586 easily. The following is the detailed procedure to determine the greatest common factor of fractions 444/74, 2184/178.
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 444/74,2184/178?
Given fractions are 444/74,2184/178
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 444/74,2184/178, numerators are 444,2184
Denominators are 74,178
The GCF of 444,2184 is 12 .
LCM of 74,178 is 6586.
The greatest common factor of 444/74,2184/178 = [GCF of 444,2184]/[LCM of 74,178]= 12/6586
Therefore, the GCF of 444/74,2184/178 is 12/6586.
To find the highest common factor of 444,2184, we have to find the factors of both numbers and list the highest common factor.
The factors of 444 are 1, 2, 3, 4, 6, 12, 37, 74, 111, 148, 222, 444
The factors of 2184 are 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 273, 312, 364, 546, 728, 1092, 2184
The HCF of 444,2184 is 12.
Lets's calculate GCF of 444,2184
| 2 | 444, 2184 |
| 2 | 222, 1092 |
| 3 | 111, 546 |
| 37, 182 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 444,2184 By Matching Biggest Common Factor Method
Now, list down the factors of 444
:1,2,3,4,6,12,37,74,111,148,222,444
Now, list down the factors of 2184
:1,2,3,4,6,7,8,12,13,14,21,24,26,28,39,42,52,56,78,84,91,104,156,168,182,273,312,364,546,728,1092,2184
Greatest Common Factor
We found the factors 444,2184 . The biggest common factor number is the GCF number.
So the greatest common factor 444,2184 is 12.
Lets's calculate LCM of 74,178
| 2 | 74, 178 |
| 37, 89 |
∴ So the LCM of the given numbers is 2 x 37 x 89 = 6586
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/6586
Therefore, the GCF of Fractions 444/74,2184/178 is 12/6586
Least Common Multiple of 74,178 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 74,178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,178) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(74,178) x common factors =2 x 1 = 2
LCM(74,178) = ( 74 × 178 ) / 2
LCM(74,178) = 13172 / 2
LCM(74,178) = 6586
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 444/74, 2184/178
1. What is the HCF of 444,2184?
The HCF of 444,2184 is 12
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 444/74, 2184/178?
Answer: GCF of Numerators as per given numbers 444/74, 2184/178 is
GCF of Numerators i.e. for 444,2184 is 12
LCM of denominators i.e. for 74,178 is 6586.
Thus, GCF of Fractions is 12/6586.Finally, GCF of Fractions for 444/74, 2184/178 is 12/6586.