The number 73008

Q: Is 73008 a prime number?

No. 73008 = 2^4 × 3^3 × 13^2, so it is divisible by 2.

73008 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × $3^{3}$ × $13^{2}$ . Divisors (60): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 36, 39 … 73008.

Number

Pick any whole number from 1 to 100,000.

73008 = 2^{4} \times 3^{3} \times 13^{2}

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How to work it out

1
What is special about 73008: a Harshad number: divisible by its digit sum 18.
2
73008 is composite. Its prime factorisation is
$73008 = 2^{4} \times 3^{3} \times 13^{2}$
3
The divisors add up to 226920; without 73008 itself that is 153912, so 73008 is abundant (153912 is more than 73008). Euler's totient φ(73008) = 22464 numbers up to 73008 share no factor with it.
4
The digits of 73008 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 156 steps to reach 1.

LaTeX source of the formulas on this page

\[ 73008 = 2^{4} \times 3^{3} \times 13^{2} \]

73008 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	226920
Euler totient φ(n)	22464
Square	5330168064
Cube	389144910016512
Square root	270.199926 (= 156√3)
Digit sum / digital root	18 / 9
Collatz steps to 1	156
Scientific notation	7.3008 × $10^{4}$

73008 in other forms

Form	Value
In words	seventy-three thousand and eight
Binary (base 2)	10001110100110000
Octal (base 8)	216460
Hexadecimal (base 16)	11D30
Base 3	10201011000
As time	73008 seconds = 20 h 16 min 48 s

Is 73008 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (73008 ÷ 2 = 36504)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (73008 ÷ 3 = 24336)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (73008 ÷ 4 = 18252)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 3)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (73008 ÷ 6 = 12168)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	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 (73008 ÷ 8 = 9126)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (73008 ÷ 9 = 8112)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 8)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (73008 ÷ 12 = 6084)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 73008 a prime number?

No. 73008 = $2^{4}$ × $3^{3}$ × $13^{2}$ , so it is divisible by 2.

What are the factors of 73008?

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 36, 39, 48, 52, 54, 72, 78, 104, 108, 117, 144, 156, 169, 208, 216, 234, 312, 338, 351, 432, 468, 507, 624, 676, 702, 936, 1014, 1352, 1404, 1521, 1872, 2028, 2704, 2808, 3042, 4056, 4563, 5616, 6084, 8112, 9126, 12168, 18252, 24336, 36504, 73008.

What is 73008 in binary?

10001110100110000 (hexadecimal 11D30, octal 216460).

What is the square root of 73008?

About 270.1999, exactly 156√3.

Is 73008 divisible by 3?

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

What is special about the number 73008?

73008 is a Harshad number: divisible by its digit sum 18.