The number 72012
72012 is a composite number with 24 divisors. Its prime factorisation is × 3 × 17 × 353. Divisors (24): 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204, 353, 706, 1059, 1412 … 72012.
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How to work it out
- 1
What is special about 72012: a Harshad number: divisible by its digit sum 12.
- 2
72012 is composite. Its prime factorisation is
- 3
The divisors add up to 178416; without 72012 itself that is 106404, so 72012 is abundant (106404 is more than 72012). Euler's totient φ(72012) = 22528 numbers up to 72012 share no factor with it.
- 4
The digits of 72012 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72012 = 2^{2} \times 3 \times 17 \times 353 \]72012 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 178416 |
| Euler totient φ(n) | 22528 |
| Square | 5185728144 |
| Cube | 373434655105728 |
| Square root | 268.350517 (= 2√18003) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 143 |
| Scientific notation | 7.2012 × |
72012 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand and twelve |
| Binary (base 2) | 10001100101001100 |
| Octal (base 8) | 214514 |
| Hexadecimal (base 16) | 1194C |
| Base 3 | 10122210010 |
| As time | 72012 seconds = 20 h 0 min 12 s |
Is 72012 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72012 ÷ 2 = 36006) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72012 ÷ 3 = 24004) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72012 ÷ 4 = 18003) | 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 | Yes (72012 ÷ 6 = 12002) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72012 ÷ 12 = 6001) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72012 a prime number?
No. 72012 = × 3 × 17 × 353, so it is divisible by 2.
What are the factors of 72012?
1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204, 353, 706, 1059, 1412, 2118, 4236, 6001, 12002, 18003, 24004, 36006, 72012.
What is 72012 in binary?
10001100101001100 (hexadecimal 1194C, octal 214514).
What is the square root of 72012?
About 268.3505, exactly 2√18003.
Is 72012 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 72012?
72012 is a Harshad number: divisible by its digit sum 12.