The number 58080

Q: Is 58080 a prime number?

No. 58080 = 2^5 × 3 × 5 × 11^2, so it is divisible by 2.

58080 is a composite number with 72 divisors. Its prime factorisation is $2^{5}$ × 3 × 5 × $11^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30 … 58080.

Number

Pick any whole number from 1 to 100,000.

58080 = 2^{5} \times 3 \times 5 \times 11^{2}

Explain it step by step in chat Make a short video of it

How to work it out

1
58080 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
58080 is composite. Its prime factorisation is
$58080 = 2^{5} \times 3 \times 5 \times 11^{2}$
3
The divisors add up to 201096; without 58080 itself that is 143016, so 58080 is abundant (143016 is more than 58080). Euler's totient φ(58080) = 14080 numbers up to 58080 share no factor with it.
4
The digits of 58080 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.

LaTeX source of the formulas on this page

\[ 58080 = 2^{5} \times 3 \times 5 \times 11^{2} \]

58080 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	201096
Euler totient φ(n)	14080
Square	3373286400
Cube	195920474112000
Square root	240.997925 (= 44√30)
Digit sum / digital root	21 / 3
Collatz steps to 1	60
Scientific notation	5.808 × $10^{4}$

58080 in other forms

Form	Value
In words	fifty-eight thousand and eighty
Binary (base 2)	1110001011100000
Octal (base 8)	161340
Hexadecimal (base 16)	E2E0
Base 3	2221200010
As time	58080 seconds = 16 h 8 min 0 s

Is 58080 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (58080 ÷ 2 = 29040)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (58080 ÷ 3 = 19360)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (58080 ÷ 4 = 14520)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (58080 ÷ 5 = 11616)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (58080 ÷ 6 = 9680)	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	Yes (58080 ÷ 8 = 7260)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (58080 ÷ 10 = 5808)	A number is divisible by 10 if the last digit is 0.
11	Yes (58080 ÷ 11 = 5280)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (58080 ÷ 12 = 4840)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 58080 a prime number?

No. 58080 = $2^{5}$ × 3 × 5 × $11^{2}$ , so it is divisible by 2.

What are the factors of 58080?

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 121, 132, 160, 165, 176, 220, 240, 242, 264, 330, 352, 363, 440, 480, 484, 528, 605, 660, 726, 880, 968, 1056, 1210, 1320, 1452, 1760, 1815, 1936, 2420, 2640, 2904, 3630, 3872, 4840, 5280, 5808, 7260, 9680, 11616, 14520, 19360, 29040, 58080.

What is 58080 in binary?

1110001011100000 (hexadecimal E2E0, octal 161340).

What is the square root of 58080?

About 240.9979, exactly 44√30.

Is 58080 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 58080?

It is a composite number with 72 divisors.