The number 73600
73600 is a composite number with 48 divisors. Its prime factorisation is × × 23. Divisors (48): 1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 32, 40, 46, 50, 64, 80 … 73600.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 73600: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.
- 2
73600 is composite. Its prime factorisation is
- 3
The divisors add up to 189720; without 73600 itself that is 116120, so 73600 is abundant (116120 is more than 73600). Euler's totient φ(73600) = 28160 numbers up to 73600 share no factor with it.
- 4
The digits of 73600 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73600 = 2^{7} \times 5^{2} \times 23 \]73600 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 189720 |
| Euler totient φ(n) | 28160 |
| Square | 5416960000 |
| Cube | 398688256000000 |
| Square root | 271.293199 (= 40√46) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.36 × |
73600 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand six hundred |
| Binary (base 2) | 10001111110000000 |
| Octal (base 8) | 217600 |
| Hexadecimal (base 16) | 11F80 |
| Base 3 | 10201221221 |
| As time | 73600 seconds = 20 h 26 min 40 s |
Is 73600 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73600 ÷ 2 = 36800) | 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 (73600 ÷ 4 = 18400) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (73600 ÷ 5 = 14720) | 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 2) | 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 (73600 ÷ 8 = 9200) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (73600 ÷ 10 = 7360) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 73600 a prime number?
No. 73600 = × × 23, so it is divisible by 2.
What are the factors of 73600?
1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 32, 40, 46, 50, 64, 80, 92, 100, 115, 128, 160, 184, 200, 230, 320, 368, 400, 460, 575, 640, 736, 800, 920, 1150, 1472, 1600, 1840, 2300, 2944, 3200, 3680, 4600, 7360, 9200, 14720, 18400, 36800, 73600.
What is 73600 in binary?
10001111110000000 (hexadecimal 11F80, octal 217600).
What is the square root of 73600?
About 271.2932, exactly 40√46.
Is 73600 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 73600?
73600 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.