GCF of 294/54, 504/53, 642/51
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 294/54, 504/53, 642/51 i.e 6/48654 easily. The following is the detailed procedure to determine the greatest common factor of fractions 294/54, 504/53, 642/51.
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 294/54,504/53,642/51?
Given fractions are 294/54,504/53,642/51
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 294/54,504/53,642/51, numerators are 294,504,642
Denominators are 54,53,51
The GCF of 294,504,642 is 6 .
LCM of 54,53,51 is 48654.
The greatest common factor of 294/54,504/53,642/51 = [GCF of 294,504,642]/[LCM of 54,53,51]= 6/48654
Therefore, the GCF of 294/54,504/53,642/51 is 6/48654.
To find the highest common factor of 294,504,642, we have to find the factors of both numbers and list the highest common factor.
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
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 factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The HCF of 294,504,642 is 6.
Lets's calculate GCF of 294,504,642
| 2 | 294, 504, 642 |
| 3 | 147, 252, 321 |
| 49, 84, 107 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 294,504,642 By Matching Biggest Common Factor Method
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
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
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
Greatest Common Factor
We found the factors 294,504,642 . The biggest common factor number is the GCF number.
So the greatest common factor 294,504,642 is 6.
Lets's calculate LCM of 54,53,51
| 3 | 54, 53, 51 |
| 18, 53, 17 |
∴ So the LCM of the given numbers is 3 x 18 x 53 x 17 = 48654
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/48654
Therefore, the GCF of Fractions 294/54,504/53,642/51 is 6/48654
Least Common Multiple of 54,53,51 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 54,53,51 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,53,51) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(54,53,51) x common factors =1 x 3 = 3
LCM(54,53,51) = ( 54 × 53 × 51 ) / 3
LCM(54,53,51) = 145962 / 3
LCM(54,53,51) = 48654
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FAQs on GCF of Fractions of 294/54, 504/53, 642/51
1. What is the HCF of 294,504,642?
The HCF of 294,504,642 is 6
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 294/54, 504/53, 642/51?
Answer: GCF of Numerators as per given numbers 294/54, 504/53, 642/51 is
GCF of Numerators i.e. for 294,504,642 is 6
LCM of denominators i.e. for 54,53,51 is 48654.
Thus, GCF of Fractions is 6/48654.Finally, GCF of Fractions for 294/54, 504/53, 642/51 is 6/48654.