GCF of 586/564, 820/624
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 586/564, 820/624 i.e 2/29328 easily. The following is the detailed procedure to determine the greatest common factor of fractions 586/564, 820/624.
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 586/564,820/624?
Given fractions are 586/564,820/624
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 586/564,820/624, numerators are 586,820
Denominators are 564,624
The GCF of 586,820 is 2 .
LCM of 564,624 is 29328.
The greatest common factor of 586/564,820/624 = [GCF of 586,820]/[LCM of 564,624]= 2/29328
Therefore, the GCF of 586/564,820/624 is 2/29328.
To find the highest common factor of 586,820, we have to find the factors of both numbers and list the highest common factor.
The factors of 586 are 1, 2, 293, 586
The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820
The HCF of 586,820 is 2.
Lets's calculate GCF of 586,820
| 2 | 586, 820 |
| 293, 410 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 586,820 By Matching Biggest Common Factor Method
Now, list down the factors of 586
:1,2,293,586
Now, list down the factors of 820
:1,2,4,5,10,20,41,82,164,205,410,820
Greatest Common Factor
We found the factors 586,820 . The biggest common factor number is the GCF number.
So the greatest common factor 586,820 is 2.
Lets's calculate LCM of 564,624
| 2 | 564, 624 |
| 2 | 282, 312 |
| 3 | 141, 156 |
| 47, 52 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 47 x 52 = 29328
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/29328
Therefore, the GCF of Fractions 586/564,820/624 is 2/29328
Least Common Multiple of 564,624 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 564,624 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,624) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(564,624) x common factors =12 x 1 = 12
LCM(564,624) = ( 564 × 624 ) / 12
LCM(564,624) = 351936 / 12
LCM(564,624) = 29328
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FAQs on GCF of Fractions of 586/564, 820/624
1. What is the HCF of 586,820?
The HCF of 586,820 is 2
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 586/564, 820/624?
Answer: GCF of Numerators as per given numbers 586/564, 820/624 is
GCF of Numerators i.e. for 586,820 is 2
LCM of denominators i.e. for 564,624 is 29328.
Thus, GCF of Fractions is 2/29328.Finally, GCF of Fractions for 586/564, 820/624 is 2/29328.