GCF of 557/78, 738/72, 504/75
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 557/78, 738/72, 504/75 i.e 1/23400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 557/78, 738/72, 504/75.
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 557/78,738/72,504/75?
Given fractions are 557/78,738/72,504/75
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 557/78,738/72,504/75, numerators are 557,738,504
Denominators are 78,72,75
The GCF of 557,738,504 is 1 .
LCM of 78,72,75 is 23400.
The greatest common factor of 557/78,738/72,504/75 = [GCF of 557,738,504]/[LCM of 78,72,75]= 1/23400
Therefore, the GCF of 557/78,738/72,504/75 is 1/23400.
To find the highest common factor of 557,738,504, we have to find the factors of both numbers and list the highest common factor.
The factors of 557 are 1, 557
The factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The HCF of 557,738,504 is 1.
Lets's calculate GCF of 557,738,504
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 557,738,504 By Matching Biggest Common Factor Method
Now, list down the factors of 557
:1,557
Now, list down the factors of 738
:1,2,3,6,9,18,41,82,123,246,369,738
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
Greatest Common Factor
We found the factors 557,738,504 . The biggest common factor number is the GCF number.
So the greatest common factor 557,738,504 is 1.
Lets's calculate LCM of 78,72,75
| 2 | 78, 72, 75 |
| 3 | 39, 36, 75 |
| 13, 12, 25 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 12 x 25 = 23400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23400
Therefore, the GCF of Fractions 557/78,738/72,504/75 is 1/23400
Least Common Multiple of 78,72,75 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 78,72,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,72,75) = 3
common factors(in case of two or more numbers have common factors) = 6
GCF(78,72,75) x common factors =3 x 6 = 18
LCM(78,72,75) = ( 78 × 72 × 75 ) / 18
LCM(78,72,75) = 421200 / 18
LCM(78,72,75) = 23400
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FAQs on GCF of Fractions of 557/78, 738/72, 504/75
1. What is the HCF of 557,738,504?
The HCF of 557,738,504 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 557/78, 738/72, 504/75?
Answer: GCF of Numerators as per given numbers 557/78, 738/72, 504/75 is
GCF of Numerators i.e. for 557,738,504 is 1
LCM of denominators i.e. for 78,72,75 is 23400.
Thus, GCF of Fractions is 1/23400.Finally, GCF of Fractions for 557/78, 738/72, 504/75 is 1/23400.