GCF of 972/182, 864/624, 219/367
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 972/182, 864/624, 219/367 i.e 3/1603056 easily. The following is the detailed procedure to determine the greatest common factor of fractions 972/182, 864/624, 219/367.
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 972/182,864/624,219/367?
Given fractions are 972/182,864/624,219/367
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 972/182,864/624,219/367, numerators are 972,864,219
Denominators are 182,624,367
The GCF of 972,864,219 is 3 .
LCM of 182,624,367 is 1603056.
The greatest common factor of 972/182,864/624,219/367 = [GCF of 972,864,219]/[LCM of 182,624,367]= 3/1603056
Therefore, the GCF of 972/182,864/624,219/367 is 3/1603056.
To find the highest common factor of 972,864,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
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 factors of 219 are 1, 3, 73, 219
The HCF of 972,864,219 is 3.
Lets's calculate GCF of 972,864,219
| 3 | 972, 864, 219 |
| 324, 288, 73 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 972,864,219 By Matching Biggest Common Factor Method
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
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
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 972,864,219 . The biggest common factor number is the GCF number.
So the greatest common factor 972,864,219 is 3.
Lets's calculate LCM of 182,624,367
| 2 | 182, 624, 367 |
| 13 | 91, 312, 367 |
| 7, 24, 367 |
∴ So the LCM of the given numbers is 2 x 13 x 7 x 24 x 367 = 1603056
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1603056
Therefore, the GCF of Fractions 972/182,864/624,219/367 is 3/1603056
Least Common Multiple of 182,624,367 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 182,624,367 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(182,624,367) = 1
common factors(in case of two or more numbers have common factors) = 26
GCF(182,624,367) x common factors =1 x 26 = 26
LCM(182,624,367) = ( 182 × 624 × 367 ) / 26
LCM(182,624,367) = 41679456 / 26
LCM(182,624,367) = 1603056
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 972/182, 864/624, 219/367
1. What is the HCF of 972,864,219?
The HCF of 972,864,219 is 3
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 972/182, 864/624, 219/367?
Answer: GCF of Numerators as per given numbers 972/182, 864/624, 219/367 is
GCF of Numerators i.e. for 972,864,219 is 3
LCM of denominators i.e. for 182,624,367 is 1603056.
Thus, GCF of Fractions is 3/1603056.Finally, GCF of Fractions for 972/182, 864/624, 219/367 is 3/1603056.