GCF of 1/64, 27/32, 70/189, 819/546
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1/64, 27/32, 70/189, 819/546 i.e 1/157248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1/64, 27/32, 70/189, 819/546.
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 1/64,27/32,70/189,819/546?
Given fractions are 1/64,27/32,70/189,819/546
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 1/64,27/32,70/189,819/546, numerators are 1,27,70,819
Denominators are 64,32,189,546
The GCF of 1,27,70,819 is 1 .
LCM of 64,32,189,546 is 157248.
The greatest common factor of 1/64,27/32,70/189,819/546 = [GCF of 1,27,70,819]/[LCM of 64,32,189,546]= 1/157248
Therefore, the GCF of 1/64,27/32,70/189,819/546 is 1/157248.
To find the highest common factor of 1,27,70,819, we have to find the factors of both numbers and list the highest common factor.
The factors of 1 are 1
The factors of 27 are 1, 3, 9, 27
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The HCF of 1,27,70,819 is 1.
Lets's calculate GCF of 1,27,70,819
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1,27,70,819 By Matching Biggest Common Factor Method
Now, list down the factors of 1
:1
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Greatest Common Factor
We found the factors 1,27,70,819 . The biggest common factor number is the GCF number.
So the greatest common factor 1,27,70,819 is 1.
Lets's calculate LCM of 64,32,189,546
| 2 | 64, 32, 189, 546 |
| 2 | 32, 16, 189, 273 |
| 2 | 8, 16, 189, 273 |
| 2 | 4, 8, 189, 273 |
| 2 | 2, 4, 189, 273 |
| 3 | 1, 2, 189, 273 |
| 7 | 1, 2, 63, 91 |
| 1, 2, 9, 13 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 7 x 1 x 2 x 9 x 13 = 157248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/157248
Therefore, the GCF of Fractions 1/64,27/32,70/189,819/546 is 1/157248
Least Common Multiple of 64,32,189,546 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 64,32,189,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,32,189,546) = 1
common factors(in case of two or more numbers have common factors) = 1344
GCF(64,32,189,546) x common factors =1 x 1344 = 1344
LCM(64,32,189,546) = ( 64 × 32 × 189 × 546 ) / 1344
LCM(64,32,189,546) = 211341312 / 1344
LCM(64,32,189,546) = 157248
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FAQs on GCF of Fractions of 1/64, 27/32, 70/189, 819/546
1. What is the HCF of 1,27,70,819?
The HCF of 1,27,70,819 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 1/64, 27/32, 70/189, 819/546?
Answer: GCF of Numerators as per given numbers 1/64, 27/32, 70/189, 819/546 is
GCF of Numerators i.e. for 1,27,70,819 is 1
LCM of denominators i.e. for 64,32,189,546 is 157248.
Thus, GCF of Fractions is 1/157248.Finally, GCF of Fractions for 1/64, 27/32, 70/189, 819/546 is 1/157248.