GCF of 23/21, 348/81, 864/165
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 23/21, 348/81, 864/165 i.e 1/31185 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/21, 348/81, 864/165.
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 23/21,348/81,864/165?
Given fractions are 23/21,348/81,864/165
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 23/21,348/81,864/165, numerators are 23,348,864
Denominators are 21,81,165
The GCF of 23,348,864 is 1 .
LCM of 21,81,165 is 31185.
The greatest common factor of 23/21,348/81,864/165 = [GCF of 23,348,864]/[LCM of 21,81,165]= 1/31185
Therefore, the GCF of 23/21,348/81,864/165 is 1/31185.
To find the highest common factor of 23,348,864, we have to find the factors of both numbers and list the highest common factor.
The factors of 23 are 1, 23
The factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The HCF of 23,348,864 is 1.
Lets's calculate GCF of 23,348,864
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 23,348,864 By Matching Biggest Common Factor Method
Now, list down the factors of 23
:1,23
Now, list down the factors of 348
:1,2,3,4,6,12,29,58,87,116,174,348
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Greatest Common Factor
We found the factors 23,348,864 . The biggest common factor number is the GCF number.
So the greatest common factor 23,348,864 is 1.
Lets's calculate LCM of 21,81,165
| 3 | 21, 81, 165 |
| 7, 27, 55 |
∴ So the LCM of the given numbers is 3 x 7 x 27 x 55 = 31185
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31185
Therefore, the GCF of Fractions 23/21,348/81,864/165 is 1/31185
Least Common Multiple of 21,81,165 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 21,81,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,81,165) = 3
common factors(in case of two or more numbers have common factors) = 3
GCF(21,81,165) x common factors =3 x 3 = 9
LCM(21,81,165) = ( 21 × 81 × 165 ) / 9
LCM(21,81,165) = 280665 / 9
LCM(21,81,165) = 31185
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FAQs on GCF of Fractions of 23/21, 348/81, 864/165
1. What is the HCF of 23,348,864?
The HCF of 23,348,864 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 23/21, 348/81, 864/165?
Answer: GCF of Numerators as per given numbers 23/21, 348/81, 864/165 is
GCF of Numerators i.e. for 23,348,864 is 1
LCM of denominators i.e. for 21,81,165 is 31185.
Thus, GCF of Fractions is 1/31185.Finally, GCF of Fractions for 23/21, 348/81, 864/165 is 1/31185.