The number 72512
72512 is a composite number with 28 divisors. Its prime factorisation is × 11 × 103. Divisors (28): 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 103, 176, 206, 352, 412 … 72512.
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How to work it out
- 1
72512 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72512 is composite. Its prime factorisation is
- 3
The divisors add up to 158496; without 72512 itself that is 85984, so 72512 is abundant (85984 is more than 72512). Euler's totient φ(72512) = 32640 numbers up to 72512 share no factor with it.
- 4
The digits of 72512 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72512 = 2^{6} \times 11 \times 103 \]72512 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 158496 |
| Euler totient φ(n) | 32640 |
| Square | 5257990144 |
| Cube | 381267381321728 |
| Square root | 269.280523 (= 8√1133) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 68 |
| Scientific notation | 7.2512 × |
72512 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand five hundred and twelve |
| Binary (base 2) | 10001101101000000 |
| Octal (base 8) | 215500 |
| Hexadecimal (base 16) | 11B40 |
| Base 3 | 10200110122 |
| As time | 72512 seconds = 20 h 8 min 32 s |
Is 72512 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72512 ÷ 2 = 36256) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72512 ÷ 4 = 18128) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 (72512 ÷ 8 = 9064) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (72512 ÷ 11 = 6592) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72512 a prime number?
No. 72512 = × 11 × 103, so it is divisible by 2.
What are the factors of 72512?
1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 103, 176, 206, 352, 412, 704, 824, 1133, 1648, 2266, 3296, 4532, 6592, 9064, 18128, 36256, 72512.
What is 72512 in binary?
10001101101000000 (hexadecimal 11B40, octal 215500).
What is the square root of 72512?
About 269.2805, exactly 8√1133.
Is 72512 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 72512?
It is a composite number with 28 divisors.