GCF of 588/585, 507/720
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 588/585, 507/720 i.e 3/9360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 588/585, 507/720.
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 588/585,507/720?
Given fractions are 588/585,507/720
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 588/585,507/720, numerators are 588,507
Denominators are 585,720
The GCF of 588,507 is 3 .
LCM of 585,720 is 9360.
The greatest common factor of 588/585,507/720 = [GCF of 588,507]/[LCM of 585,720]= 3/9360
Therefore, the GCF of 588/585,507/720 is 3/9360.
To find the highest common factor of 588,507, we have to find the factors of both numbers and list the highest common factor.
The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
The factors of 507 are 1, 3, 13, 39, 169, 507
The HCF of 588,507 is 3.
Lets's calculate GCF of 588,507
| 3 | 588, 507 |
| 196, 169 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 588,507 By Matching Biggest Common Factor Method
Now, list down the factors of 588
:1,2,3,4,6,7,12,14,21,28,42,49,84,98,147,196,294,588
Now, list down the factors of 507
:1,3,13,39,169,507
Greatest Common Factor
We found the factors 588,507 . The biggest common factor number is the GCF number.
So the greatest common factor 588,507 is 3.
Lets's calculate LCM of 585,720
| 3 | 585, 720 |
| 3 | 195, 240 |
| 5 | 65, 80 |
| 13, 16 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 13 x 16 = 9360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/9360
Therefore, the GCF of Fractions 588/585,507/720 is 3/9360
Least Common Multiple of 585,720 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 585,720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(585,720) = 45
common factors(in case of two or more numbers have common factors) = 1
GCF(585,720) x common factors =45 x 1 = 45
LCM(585,720) = ( 585 × 720 ) / 45
LCM(585,720) = 421200 / 45
LCM(585,720) = 9360
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FAQs on GCF of Fractions of 588/585, 507/720
1. What is the HCF of 588,507?
The HCF of 588,507 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 588/585, 507/720?
Answer: GCF of Numerators as per given numbers 588/585, 507/720 is
GCF of Numerators i.e. for 588,507 is 3
LCM of denominators i.e. for 585,720 is 9360.
Thus, GCF of Fractions is 3/9360.Finally, GCF of Fractions for 588/585, 507/720 is 3/9360.