GCF of 123/414, 834/144
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 123/414, 834/144 i.e 3/3312 easily. The following is the detailed procedure to determine the greatest common factor of fractions 123/414, 834/144.
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 123/414,834/144?
Given fractions are 123/414,834/144
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 123/414,834/144, numerators are 123,834
Denominators are 414,144
The GCF of 123,834 is 3 .
LCM of 414,144 is 3312.
The greatest common factor of 123/414,834/144 = [GCF of 123,834]/[LCM of 414,144]= 3/3312
Therefore, the GCF of 123/414,834/144 is 3/3312.
To find the highest common factor of 123,834, we have to find the factors of both numbers and list the highest common factor.
The factors of 123 are 1, 3, 41, 123
The factors of 834 are 1, 2, 3, 6, 139, 278, 417, 834
The HCF of 123,834 is 3.
Lets's calculate GCF of 123,834
| 3 | 123, 834 |
| 41, 278 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 123,834 By Matching Biggest Common Factor Method
Now, list down the factors of 123
:1,3,41,123
Now, list down the factors of 834
:1,2,3,6,139,278,417,834
Greatest Common Factor
We found the factors 123,834 . The biggest common factor number is the GCF number.
So the greatest common factor 123,834 is 3.
Lets's calculate LCM of 414,144
| 2 | 414, 144 |
| 3 | 207, 72 |
| 3 | 69, 24 |
| 23, 8 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 23 x 8 = 3312
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3312
Therefore, the GCF of Fractions 123/414,834/144 is 3/3312
Least Common Multiple of 414,144 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 414,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,144) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(414,144) x common factors =18 x 1 = 18
LCM(414,144) = ( 414 × 144 ) / 18
LCM(414,144) = 59616 / 18
LCM(414,144) = 3312
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FAQs on GCF of Fractions of 123/414, 834/144
1. What is the HCF of 123,834?
The HCF of 123,834 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 123/414, 834/144?
Answer: GCF of Numerators as per given numbers 123/414, 834/144 is
GCF of Numerators i.e. for 123,834 is 3
LCM of denominators i.e. for 414,144 is 3312.
Thus, GCF of Fractions is 3/3312.Finally, GCF of Fractions for 123/414, 834/144 is 3/3312.