GCF of 468/189, 546/959
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 468/189, 546/959 i.e 78/25893 easily. The following is the detailed procedure to determine the greatest common factor of fractions 468/189, 546/959.
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 468/189,546/959?
Given fractions are 468/189,546/959
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 468/189,546/959, numerators are 468,546
Denominators are 189,959
The GCF of 468,546 is 78 .
LCM of 189,959 is 25893.
The greatest common factor of 468/189,546/959 = [GCF of 468,546]/[LCM of 189,959]= 78/25893
Therefore, the GCF of 468/189,546/959 is 78/25893.
To find the highest common factor of 468,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 468,546 is 78.
Lets's calculate GCF of 468,546
| 2 | 468, 546 |
| 3 | 234, 273 |
| 13 | 78, 91 |
| 6, 7 |
∴ So the GCF of the given numbers is 2 x 3 x 13 = 78
Greatest Common Factor of 468,546 By Matching Biggest Common Factor Method
Now, list down the factors of 468
:1,2,3,4,6,9,12,13,18,26,36,39,52,78,117,156,234,468
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 468,546 . The biggest common factor number is the GCF number.
So the greatest common factor 468,546 is 78.
Lets's calculate LCM of 189,959
| 7 | 189, 959 |
| 27, 137 |
∴ So the LCM of the given numbers is 7 x 27 x 137 = 25893
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 78/25893
Therefore, the GCF of Fractions 468/189,546/959 is 78/25893
Least Common Multiple of 189,959 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 189,959 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(189,959) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(189,959) x common factors =7 x 1 = 7
LCM(189,959) = ( 189 × 959 ) / 7
LCM(189,959) = 181251 / 7
LCM(189,959) = 25893
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FAQs on GCF of Fractions of 468/189, 546/959
1. What is the HCF of 468,546?
The HCF of 468,546 is 78
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 468/189, 546/959?
Answer: GCF of Numerators as per given numbers 468/189, 546/959 is
GCF of Numerators i.e. for 468,546 is 78
LCM of denominators i.e. for 189,959 is 25893.
Thus, GCF of Fractions is 78/25893.Finally, GCF of Fractions for 468/189, 546/959 is 78/25893.