The number 73080

Q: Is 73080 a prime number?

No. 73080 = 2^3 × 3^2 × 5 × 7 × 29, so it is divisible by 2.

73080 is a composite number with 96 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × 5 × 7 × 29. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21 … 73080.

Number

Pick any whole number from 1 to 100,000.

73080 = 2^{3} \times 3^{2} \times 5 \times 7 \times 29

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How to work it out

1
What is special about 73080: a Harshad number: divisible by its digit sum 18.
2
73080 is composite. Its prime factorisation is
$73080 = 2^{3} \times 3^{2} \times 5 \times 7 \times 29$
3
The divisors add up to 280800; without 73080 itself that is 207720, so 73080 is abundant (207720 is more than 73080). Euler's totient φ(73080) = 16128 numbers up to 73080 share no factor with it.
4
The digits of 73080 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 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 73080 = 2^{3} \times 3^{2} \times 5 \times 7 \times 29 \]

73080 at a glance

Property	Value
Type	composite
Number of divisors	96
Sum of divisors	280800
Euler totient φ(n)	16128
Square	5340686400
Cube	390297362112000
Square root	270.333128 (= 6√2030)
Digit sum / digital root	18 / 9
Collatz steps to 1	63
Scientific notation	7.308 × $10^{4}$

73080 in other forms

Form	Value
In words	seventy-three thousand and eighty
Binary (base 2)	10001110101111000
Octal (base 8)	216570
Hexadecimal (base 16)	11D78
Base 3	10201020200
As time	73080 seconds = 20 h 18 min 0 s

Is 73080 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (73080 ÷ 2 = 36540)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (73080 ÷ 3 = 24360)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (73080 ÷ 4 = 18270)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (73080 ÷ 5 = 14616)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (73080 ÷ 6 = 12180)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (73080 ÷ 7 = 10440)	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 (73080 ÷ 8 = 9135)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (73080 ÷ 9 = 8120)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (73080 ÷ 10 = 7308)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 7)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (73080 ÷ 12 = 6090)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 73080 a prime number?

No. 73080 = $2^{3}$ × $3^{2}$ × 5 × 7 × 29, so it is divisible by 2.

What are the factors of 73080?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 29, 30, 35, 36, 40, 42, 45, 56, 58, 60, 63, 70, 72, 84, 87, 90, 105, 116, 120, 126, 140, 145, 168, 174, 180, 203, 210, 232, 252, 261, 280, 290, 315, 348, 360, 406, 420, 435, 504, 522, 580, 609, 630, 696, 812, 840, 870, 1015, 1044, 1160, 1218, 1260, 1305, 1624, 1740, 1827, 2030, 2088, 2436, 2520, 2610, 3045, 3480, 3654, 4060, 4872, 5220, 6090, 7308, 8120, 9135, 10440, 12180, 14616, 18270, 24360, 36540, 73080.

What is 73080 in binary?

10001110101111000 (hexadecimal 11D78, octal 216570).

What is the square root of 73080?

About 270.3331, exactly 6√2030.

Is 73080 divisible by 3?

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

What is special about the number 73080?

73080 is a Harshad number: divisible by its digit sum 18.