The number 58500

Q: Is 58500 a prime number?

No. 58500 = 2^2 × 3^2 × 5^3 × 13, so it is divisible by 2.

58500 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × $5^{3}$ × 13. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 25, 26, 30 … 58500.

Number

Pick any whole number from 1 to 100,000.

58500 = 2^{2} \times 3^{2} \times 5^{3} \times 13

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How to work it out

1
What is special about 58500: a Harshad number: divisible by its digit sum 18.
2
58500 is composite. Its prime factorisation is
$58500 = 2^{2} \times 3^{2} \times 5^{3} \times 13$
3
The divisors add up to 198744; without 58500 itself that is 140244, so 58500 is abundant (140244 is more than 58500). Euler's totient φ(58500) = 14400 numbers up to 58500 share no factor with it.
4
The digits of 58500 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 47 steps to reach 1.

LaTeX source of the formulas on this page

\[ 58500 = 2^{2} \times 3^{2} \times 5^{3} \times 13 \]

58500 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	198744
Euler totient φ(n)	14400
Square	3422250000
Cube	200201625000000
Square root	241.867732 (= 30√65)
Digit sum / digital root	18 / 9
Collatz steps to 1	47
Scientific notation	5.85 × $10^{4}$

58500 in other forms

Form	Value
In words	fifty-eight thousand five hundred
Binary (base 2)	1110010010000100
Octal (base 8)	162204
Hexadecimal (base 16)	E484
Base 3	2222020200
As time	58500 seconds = 16 h 15 min 0 s

Is 58500 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (58500 ÷ 2 = 29250)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (58500 ÷ 3 = 19500)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (58500 ÷ 4 = 14625)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (58500 ÷ 5 = 11700)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (58500 ÷ 6 = 9750)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (58500 ÷ 9 = 6500)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (58500 ÷ 10 = 5850)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (58500 ÷ 12 = 4875)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 58500 a prime number?

No. 58500 = $2^{2}$ × $3^{2}$ × $5^{3}$ × 13, so it is divisible by 2.

What are the factors of 58500?

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 25, 26, 30, 36, 39, 45, 50, 52, 60, 65, 75, 78, 90, 100, 117, 125, 130, 150, 156, 180, 195, 225, 234, 250, 260, 300, 325, 375, 390, 450, 468, 500, 585, 650, 750, 780, 900, 975, 1125, 1170, 1300, 1500, 1625, 1950, 2250, 2340, 2925, 3250, 3900, 4500, 4875, 5850, 6500, 9750, 11700, 14625, 19500, 29250, 58500.

What is 58500 in binary?

1110010010000100 (hexadecimal E484, octal 162204).

What is the square root of 58500?

About 241.8677, exactly 30√65.

Is 58500 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 58500?

58500 is a Harshad number: divisible by its digit sum 18.