The number 81585

Q: Is 81585 a prime number?

No. 81585 = 3^2 × 5 × 7^2 × 37, so it is divisible by 3.

81585 is a composite number with 36 divisors. Its prime factorisation is $3^{2}$ × 5 × $7^{2}$ × 37. Divisors (36): 1, 3, 5, 7, 9, 15, 21, 35, 37, 45, 49, 63, 105, 111, 147, 185 … 81585.

Number

Pick any whole number from 1 to 100,000.

81585 = 3^{2} \times 5 \times 7^{2} \times 37

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How to work it out

1
81585 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
81585 is composite. Its prime factorisation is
$81585 = 3^{2} \times 5 \times 7^{2} \times 37$
3
The divisors add up to 168948; without 81585 itself that is 87363, so 81585 is abundant (87363 is more than 81585). Euler's totient φ(81585) = 36288 numbers up to 81585 share no factor with it.
4
The digits of 81585 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.

LaTeX source of the formulas on this page

\[ 81585 = 3^{2} \times 5 \times 7^{2} \times 37 \]

81585 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	168948
Euler totient φ(n)	36288
Square	6656112225
Cube	543038915876625
Square root	285.630881 (= 21√185)
Digit sum / digital root	27 / 9
Collatz steps to 1	120
Scientific notation	8.1585 × $10^{4}$

81585 in other forms

Form	Value
In words	eighty-one thousand five hundred and eighty-five
Binary (base 2)	10011111010110001
Octal (base 8)	237261
Hexadecimal (base 16)	13EB1
Base 3	11010220200
As time	81585 seconds = 22 h 39 min 45 s

Is 81585 divisible by 2 to 12?

Divisor	Answer	Rule
2	No (remainder 1)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (81585 ÷ 3 = 27195)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	No (remainder 1)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (81585 ÷ 5 = 16317)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 3)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (81585 ÷ 7 = 11655)	A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7.
8	No (remainder 1)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (81585 ÷ 9 = 9065)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 5)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 9)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 9)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 81585 a prime number?

No. 81585 = $3^{2}$ × 5 × $7^{2}$ × 37, so it is divisible by 3.

What are the factors of 81585?

1, 3, 5, 7, 9, 15, 21, 35, 37, 45, 49, 63, 105, 111, 147, 185, 245, 259, 315, 333, 441, 555, 735, 777, 1295, 1665, 1813, 2205, 2331, 3885, 5439, 9065, 11655, 16317, 27195, 81585.

What is 81585 in binary?

10011111010110001 (hexadecimal 13EB1, octal 237261).

What is the square root of 81585?

About 285.6309, exactly 21√185.

Is 81585 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 81585?

It is a composite number with 36 divisors.