GCF of 587/82, 462/460
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 587/82, 462/460 i.e 1/18860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 587/82, 462/460.
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 587/82,462/460?
Given fractions are 587/82,462/460
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 587/82,462/460, numerators are 587,462
Denominators are 82,460
The GCF of 587,462 is 1 .
LCM of 82,460 is 18860.
The greatest common factor of 587/82,462/460 = [GCF of 587,462]/[LCM of 82,460]= 1/18860
Therefore, the GCF of 587/82,462/460 is 1/18860.
To find the highest common factor of 587,462, we have to find the factors of both numbers and list the highest common factor.
The factors of 587 are 1, 587
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The HCF of 587,462 is 1.
Lets's calculate GCF of 587,462
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 587,462 By Matching Biggest Common Factor Method
Now, list down the factors of 587
:1,587
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Greatest Common Factor
We found the factors 587,462 . The biggest common factor number is the GCF number.
So the greatest common factor 587,462 is 1.
Lets's calculate LCM of 82,460
| 2 | 82, 460 |
| 41, 230 |
∴ So the LCM of the given numbers is 2 x 41 x 230 = 18860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18860
Therefore, the GCF of Fractions 587/82,462/460 is 1/18860
Least Common Multiple of 82,460 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 82,460 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,460) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,460) x common factors =2 x 1 = 2
LCM(82,460) = ( 82 × 460 ) / 2
LCM(82,460) = 37720 / 2
LCM(82,460) = 18860
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FAQs on GCF of Fractions of 587/82, 462/460
1. What is the HCF of 587,462?
The HCF of 587,462 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 587/82, 462/460?
Answer: GCF of Numerators as per given numbers 587/82, 462/460 is
GCF of Numerators i.e. for 587,462 is 1
LCM of denominators i.e. for 82,460 is 18860.
Thus, GCF of Fractions is 1/18860.Finally, GCF of Fractions for 587/82, 462/460 is 1/18860.