GCF of 42/16, 560/51, 994/747
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 42/16, 560/51, 994/747 i.e 14/203184 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/16, 560/51, 994/747.
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 42/16,560/51,994/747?
Given fractions are 42/16,560/51,994/747
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 42/16,560/51,994/747, numerators are 42,560,994
Denominators are 16,51,747
The GCF of 42,560,994 is 14 .
LCM of 16,51,747 is 203184.
The greatest common factor of 42/16,560/51,994/747 = [GCF of 42,560,994]/[LCM of 16,51,747]= 14/203184
Therefore, the GCF of 42/16,560/51,994/747 is 14/203184.
To find the highest common factor of 42,560,994, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The factors of 994 are 1, 2, 7, 14, 71, 142, 497, 994
The HCF of 42,560,994 is 14.
Lets's calculate GCF of 42,560,994
| 2 | 42, 560, 994 |
| 7 | 21, 280, 497 |
| 3, 40, 71 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 42,560,994 By Matching Biggest Common Factor Method
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Now, list down the factors of 994
:1,2,7,14,71,142,497,994
Greatest Common Factor
We found the factors 42,560,994 . The biggest common factor number is the GCF number.
So the greatest common factor 42,560,994 is 14.
Lets's calculate LCM of 16,51,747
| 3 | 16, 51, 747 |
| 16, 17, 249 |
∴ So the LCM of the given numbers is 3 x 16 x 17 x 249 = 203184
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/203184
Therefore, the GCF of Fractions 42/16,560/51,994/747 is 14/203184
Least Common Multiple of 16,51,747 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 16,51,747 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,51,747) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(16,51,747) x common factors =1 x 3 = 3
LCM(16,51,747) = ( 16 × 51 × 747 ) / 3
LCM(16,51,747) = 609552 / 3
LCM(16,51,747) = 203184
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FAQs on GCF of Fractions of 42/16, 560/51, 994/747
1. What is the HCF of 42,560,994?
The HCF of 42,560,994 is 14
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 42/16, 560/51, 994/747?
Answer: GCF of Numerators as per given numbers 42/16, 560/51, 994/747 is
GCF of Numerators i.e. for 42,560,994 is 14
LCM of denominators i.e. for 16,51,747 is 203184.
Thus, GCF of Fractions is 14/203184.Finally, GCF of Fractions for 42/16, 560/51, 994/747 is 14/203184.