GCF of 828/24, 144/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 828/24, 144/214 i.e 36/2568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 828/24, 144/214.
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 828/24,144/214?
Given fractions are 828/24,144/214
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 828/24,144/214, numerators are 828,144
Denominators are 24,214
The GCF of 828,144 is 36 .
LCM of 24,214 is 2568.
The greatest common factor of 828/24,144/214 = [GCF of 828,144]/[LCM of 24,214]= 36/2568
Therefore, the GCF of 828/24,144/214 is 36/2568.
To find the highest common factor of 828,144, we have to find the factors of both numbers and list the highest common factor.
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The HCF of 828,144 is 36.
Lets's calculate GCF of 828,144
| 2 | 828, 144 |
| 2 | 414, 72 |
| 3 | 207, 36 |
| 3 | 69, 12 |
| 23, 4 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Greatest Common Factor of 828,144 By Matching Biggest Common Factor Method
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Greatest Common Factor
We found the factors 828,144 . The biggest common factor number is the GCF number.
So the greatest common factor 828,144 is 36.
Lets's calculate LCM of 24,214
| 2 | 24, 214 |
| 12, 107 |
∴ So the LCM of the given numbers is 2 x 12 x 107 = 2568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/2568
Therefore, the GCF of Fractions 828/24,144/214 is 36/2568
Least Common Multiple of 24,214 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 24,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(24,214) x common factors =2 x 1 = 2
LCM(24,214) = ( 24 × 214 ) / 2
LCM(24,214) = 5136 / 2
LCM(24,214) = 2568
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FAQs on GCF of Fractions of 828/24, 144/214
1. What is the HCF of 828,144?
The HCF of 828,144 is 36
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 828/24, 144/214?
Answer: GCF of Numerators as per given numbers 828/24, 144/214 is
GCF of Numerators i.e. for 828,144 is 36
LCM of denominators i.e. for 24,214 is 2568.
Thus, GCF of Fractions is 36/2568.Finally, GCF of Fractions for 828/24, 144/214 is 36/2568.