GCF of 578/34, 438/84, 779/51
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 578/34, 438/84, 779/51 i.e 1/1428 easily. The following is the detailed procedure to determine the greatest common factor of fractions 578/34, 438/84, 779/51.
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 578/34,438/84,779/51?
Given fractions are 578/34,438/84,779/51
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 578/34,438/84,779/51, numerators are 578,438,779
Denominators are 34,84,51
The GCF of 578,438,779 is 1 .
LCM of 34,84,51 is 1428.
The greatest common factor of 578/34,438/84,779/51 = [GCF of 578,438,779]/[LCM of 34,84,51]= 1/1428
Therefore, the GCF of 578/34,438/84,779/51 is 1/1428.
To find the highest common factor of 578,438,779, we have to find the factors of both numbers and list the highest common factor.
The factors of 578 are 1, 2, 17, 34, 289, 578
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438
The factors of 779 are 1, 19, 41, 779
The HCF of 578,438,779 is 1.
Lets's calculate GCF of 578,438,779
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 578,438,779 By Matching Biggest Common Factor Method
Now, list down the factors of 578
:1,2,17,34,289,578
Now, list down the factors of 438
:1,2,3,6,73,146,219,438
Now, list down the factors of 779
:1,19,41,779
Greatest Common Factor
We found the factors 578,438,779 . The biggest common factor number is the GCF number.
So the greatest common factor 578,438,779 is 1.
Lets's calculate LCM of 34,84,51
| 2 | 34, 84, 51 |
| 3 | 17, 42, 51 |
| 17 | 17, 14, 17 |
| 1, 14, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 1 x 14 x 1 = 1428
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1428
Therefore, the GCF of Fractions 578/34,438/84,779/51 is 1/1428
Least Common Multiple of 34,84,51 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 34,84,51 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,84,51) = 1
common factors(in case of two or more numbers have common factors) = 102
GCF(34,84,51) x common factors =1 x 102 = 102
LCM(34,84,51) = ( 34 × 84 × 51 ) / 102
LCM(34,84,51) = 145656 / 102
LCM(34,84,51) = 1428
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FAQs on GCF of Fractions of 578/34, 438/84, 779/51
1. What is the HCF of 578,438,779?
The HCF of 578,438,779 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 578/34, 438/84, 779/51?
Answer: GCF of Numerators as per given numbers 578/34, 438/84, 779/51 is
GCF of Numerators i.e. for 578,438,779 is 1
LCM of denominators i.e. for 34,84,51 is 1428.
Thus, GCF of Fractions is 1/1428.Finally, GCF of Fractions for 578/34, 438/84, 779/51 is 1/1428.