The number 21072
21072 is a composite number with 20 divisors. Its prime factorisation is × 3 × 439. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 439, 878, 1317, 1756, 2634, 3512 … 21072.
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How to work it out
- 1
What is special about 21072: a Harshad number: divisible by its digit sum 12.
- 2
21072 is composite. Its prime factorisation is
- 3
The divisors add up to 54560; without 21072 itself that is 33488, so 21072 is abundant (33488 is more than 21072). Euler's totient φ(21072) = 7008 numbers up to 21072 share no factor with it.
- 4
The digits of 21072 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 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21072 = 2^{4} \times 3 \times 439 \]21072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 54560 |
| Euler totient φ(n) | 7008 |
| Square | 444029184 |
| Cube | 9356582965248 |
| Square root | 145.161978 (= 4√1317) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.1072 × |
21072 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand and seventy-two |
| Binary (base 2) | 101001001010000 |
| Octal (base 8) | 51120 |
| Hexadecimal (base 16) | 5250 |
| Base 3 | 1001220110 |
| As time | 21072 seconds = 5 h 51 min 12 s |
Is 21072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21072 ÷ 2 = 10536) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21072 ÷ 3 = 7024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21072 ÷ 4 = 5268) | 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 (21072 ÷ 6 = 3512) | 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 (21072 ÷ 8 = 2634) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21072 ÷ 12 = 1756) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21072 a prime number?
No. 21072 = × 3 × 439, so it is divisible by 2.
What are the factors of 21072?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 439, 878, 1317, 1756, 2634, 3512, 5268, 7024, 10536, 21072.
What is 21072 in binary?
101001001010000 (hexadecimal 5250, octal 51120).
What is the square root of 21072?
About 145.1620, exactly 4√1317.
Is 21072 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 21072?
21072 is a Harshad number: divisible by its digit sum 12.