GCF of 591/12, 609/52, 972/66
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 591/12, 609/52, 972/66 i.e 3/1716 easily. The following is the detailed procedure to determine the greatest common factor of fractions 591/12, 609/52, 972/66.
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 591/12,609/52,972/66?
Given fractions are 591/12,609/52,972/66
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 591/12,609/52,972/66, numerators are 591,609,972
Denominators are 12,52,66
The GCF of 591,609,972 is 3 .
LCM of 12,52,66 is 1716.
The greatest common factor of 591/12,609/52,972/66 = [GCF of 591,609,972]/[LCM of 12,52,66]= 3/1716
Therefore, the GCF of 591/12,609/52,972/66 is 3/1716.
To find the highest common factor of 591,609,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 591 are 1, 3, 197, 591
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 591,609,972 is 3.
Lets's calculate GCF of 591,609,972
| 3 | 591, 609, 972 |
| 197, 203, 324 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 591,609,972 By Matching Biggest Common Factor Method
Now, list down the factors of 591
:1,3,197,591
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
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
Greatest Common Factor
We found the factors 591,609,972 . The biggest common factor number is the GCF number.
So the greatest common factor 591,609,972 is 3.
Lets's calculate LCM of 12,52,66
| 2 | 12, 52, 66 |
| 2 | 6, 26, 33 |
| 3 | 3, 13, 33 |
| 1, 13, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 1 x 13 x 11 = 1716
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1716
Therefore, the GCF of Fractions 591/12,609/52,972/66 is 3/1716
Least Common Multiple of 12,52,66 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 12,52,66 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,52,66) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(12,52,66) x common factors =2 x 12 = 24
LCM(12,52,66) = ( 12 × 52 × 66 ) / 24
LCM(12,52,66) = 41184 / 24
LCM(12,52,66) = 1716
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FAQs on GCF of Fractions of 591/12, 609/52, 972/66
1. What is the HCF of 591,609,972?
The HCF of 591,609,972 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 591/12, 609/52, 972/66?
Answer: GCF of Numerators as per given numbers 591/12, 609/52, 972/66 is
GCF of Numerators i.e. for 591,609,972 is 3
LCM of denominators i.e. for 12,52,66 is 1716.
Thus, GCF of Fractions is 3/1716.Finally, GCF of Fractions for 591/12, 609/52, 972/66 is 3/1716.