The number 73408
73408 is a composite number with 28 divisors. Its prime factorisation is × 31 × 37. Divisors (28): 1, 2, 4, 8, 16, 31, 32, 37, 62, 64, 74, 124, 148, 248, 296, 496 … 73408.
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How to work it out
- 1
73408 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
73408 is composite. Its prime factorisation is
- 3
The divisors add up to 154432; without 73408 itself that is 81024, so 73408 is abundant (81024 is more than 73408). Euler's totient φ(73408) = 34560 numbers up to 73408 share no factor with it.
- 4
The digits of 73408 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73408 = 2^{6} \times 31 \times 37 \]73408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 154432 |
| Euler totient φ(n) | 34560 |
| Square | 5388734464 |
| Cube | 395576219533312 |
| Square root | 270.939108 (= 8√1147) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 63 |
| Scientific notation | 7.3408 × |
73408 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand four hundred and eight |
| Binary (base 2) | 10001111011000000 |
| Octal (base 8) | 217300 |
| Hexadecimal (base 16) | 11EC0 |
| Base 3 | 10201200211 |
| As time | 73408 seconds = 20 h 23 min 28 s |
Is 73408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73408 ÷ 2 = 36704) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73408 ÷ 4 = 18352) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (73408 ÷ 8 = 9176) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73408 a prime number?
No. 73408 = × 31 × 37, so it is divisible by 2.
What are the factors of 73408?
1, 2, 4, 8, 16, 31, 32, 37, 62, 64, 74, 124, 148, 248, 296, 496, 592, 992, 1147, 1184, 1984, 2294, 2368, 4588, 9176, 18352, 36704, 73408.
What is 73408 in binary?
10001111011000000 (hexadecimal 11EC0, octal 217300).
What is the square root of 73408?
About 270.9391, exactly 8√1147.
Is 73408 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 73408?
It is a composite number with 28 divisors.