GCF of 52/21, 954/40, 384/560
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 52/21, 954/40, 384/560 i.e 2/1680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 52/21, 954/40, 384/560.
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 52/21,954/40,384/560?
Given fractions are 52/21,954/40,384/560
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 52/21,954/40,384/560, numerators are 52,954,384
Denominators are 21,40,560
The GCF of 52,954,384 is 2 .
LCM of 21,40,560 is 1680.
The greatest common factor of 52/21,954/40,384/560 = [GCF of 52,954,384]/[LCM of 21,40,560]= 2/1680
Therefore, the GCF of 52/21,954/40,384/560 is 2/1680.
To find the highest common factor of 52,954,384, we have to find the factors of both numbers and list the highest common factor.
The factors of 52 are 1, 2, 4, 13, 26, 52
The factors of 954 are 1, 2, 3, 6, 9, 18, 53, 106, 159, 318, 477, 954
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The HCF of 52,954,384 is 2.
Lets's calculate GCF of 52,954,384
| 2 | 52, 954, 384 |
| 26, 477, 192 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 52,954,384 By Matching Biggest Common Factor Method
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 954
:1,2,3,6,9,18,53,106,159,318,477,954
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Greatest Common Factor
We found the factors 52,954,384 . The biggest common factor number is the GCF number.
So the greatest common factor 52,954,384 is 2.
Lets's calculate LCM of 21,40,560
| 2 | 21, 40, 560 |
| 2 | 21, 20, 280 |
| 2 | 21, 10, 140 |
| 5 | 21, 5, 70 |
| 7 | 21, 1, 14 |
| 3, 1, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 7 x 3 x 1 x 2 = 1680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1680
Therefore, the GCF of Fractions 52/21,954/40,384/560 is 2/1680
Least Common Multiple of 21,40,560 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 21,40,560 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,40,560) = 1
common factors(in case of two or more numbers have common factors) = 280
GCF(21,40,560) x common factors =1 x 280 = 280
LCM(21,40,560) = ( 21 × 40 × 560 ) / 280
LCM(21,40,560) = 470400 / 280
LCM(21,40,560) = 1680
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 52/21, 954/40, 384/560
1. What is the HCF of 52,954,384?
The HCF of 52,954,384 is 2
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 52/21, 954/40, 384/560?
Answer: GCF of Numerators as per given numbers 52/21, 954/40, 384/560 is
GCF of Numerators i.e. for 52,954,384 is 2
LCM of denominators i.e. for 21,40,560 is 1680.
Thus, GCF of Fractions is 2/1680.Finally, GCF of Fractions for 52/21, 954/40, 384/560 is 2/1680.