GCF of 210/564, 8144/2020
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 210/564, 8144/2020 i.e 2/284820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 210/564, 8144/2020.
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 210/564,8144/2020?
Given fractions are 210/564,8144/2020
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 210/564,8144/2020, numerators are 210,8144
Denominators are 564,2020
The GCF of 210,8144 is 2 .
LCM of 564,2020 is 284820.
The greatest common factor of 210/564,8144/2020 = [GCF of 210,8144]/[LCM of 564,2020]= 2/284820
Therefore, the GCF of 210/564,8144/2020 is 2/284820.
To find the highest common factor of 210,8144, we have to find the factors of both numbers and list the highest common factor.
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The factors of 8144 are 1, 2, 4, 8, 16, 509, 1018, 2036, 4072, 8144
The HCF of 210,8144 is 2.
Lets's calculate GCF of 210,8144
| 2 | 210, 8144 |
| 105, 4072 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 210,8144 By Matching Biggest Common Factor Method
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Now, list down the factors of 8144
:1,2,4,8,16,509,1018,2036,4072,8144
Greatest Common Factor
We found the factors 210,8144 . The biggest common factor number is the GCF number.
So the greatest common factor 210,8144 is 2.
Lets's calculate LCM of 564,2020
| 2 | 564, 2020 |
| 2 | 282, 1010 |
| 141, 505 |
∴ So the LCM of the given numbers is 2 x 2 x 141 x 505 = 284820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/284820
Therefore, the GCF of Fractions 210/564,8144/2020 is 2/284820
Least Common Multiple of 564,2020 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 564,2020 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,2020) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(564,2020) x common factors =4 x 1 = 4
LCM(564,2020) = ( 564 × 2020 ) / 4
LCM(564,2020) = 1139280 / 4
LCM(564,2020) = 284820
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FAQs on GCF of Fractions of 210/564, 8144/2020
1. What is the HCF of 210,8144?
The HCF of 210,8144 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 210/564, 8144/2020?
Answer: GCF of Numerators as per given numbers 210/564, 8144/2020 is
GCF of Numerators i.e. for 210,8144 is 2
LCM of denominators i.e. for 564,2020 is 284820.
Thus, GCF of Fractions is 2/284820.Finally, GCF of Fractions for 210/564, 8144/2020 is 2/284820.