The number 23772
23772 is a composite number with 24 divisors. Its prime factorisation is × 3 × 7 × 283. Divisors (24): 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 283, 566, 849, 1132 … 23772.
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How to work it out
- 1
What is special about 23772: a Harshad number: divisible by its digit sum 21.
- 2
23772 is composite. Its prime factorisation is
- 3
The divisors add up to 63616; without 23772 itself that is 39844, so 23772 is abundant (39844 is more than 23772). Euler's totient φ(23772) = 6768 numbers up to 23772 share no factor with it.
- 4
The digits of 23772 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 51 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23772 = 2^{2} \times 3 \times 7 \times 283 \]23772 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 63616 |
| Euler totient φ(n) | 6768 |
| Square | 565107984 |
| Cube | 13433746995648 |
| Square root | 154.181711 (= 2√5943) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 51 |
| Scientific notation | 2.3772 × |
23772 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand seven hundred and seventy-two |
| Binary (base 2) | 101110011011100 |
| Octal (base 8) | 56334 |
| Hexadecimal (base 16) | 5CDC |
| Base 3 | 1012121110 |
| As time | 23772 seconds = 6 h 36 min 12 s |
Is 23772 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23772 ÷ 2 = 11886) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (23772 ÷ 3 = 7924) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23772 ÷ 4 = 5943) | 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 (23772 ÷ 6 = 3962) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (23772 ÷ 7 = 3396) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (23772 ÷ 12 = 1981) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23772 a prime number?
No. 23772 = × 3 × 7 × 283, so it is divisible by 2.
What are the factors of 23772?
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 283, 566, 849, 1132, 1698, 1981, 3396, 3962, 5943, 7924, 11886, 23772.
What is 23772 in binary?
101110011011100 (hexadecimal 5CDC, octal 56334).
What is the square root of 23772?
About 154.1817, exactly 2√5943.
Is 23772 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 23772?
23772 is a Harshad number: divisible by its digit sum 21.