The number 20772
20772 is a composite number with 18 divisors. Its prime factorisation is × × 577. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 577, 1154, 1731, 2308, 3462, 5193, 6924 … 20772.
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How to work it out
- 1
What is special about 20772: a Harshad number: divisible by its digit sum 18.
- 2
20772 is composite. Its prime factorisation is
- 3
The divisors add up to 52598; without 20772 itself that is 31826, so 20772 is abundant (31826 is more than 20772). Euler's totient φ(20772) = 6912 numbers up to 20772 share no factor with it.
- 4
The digits of 20772 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 87 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20772 = 2^{2} \times 3^{2} \times 577 \]20772 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 52598 |
| Euler totient φ(n) | 6912 |
| Square | 431475984 |
| Cube | 8962619139648 |
| Square root | 144.124946 (= 6√577) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 87 |
| Scientific notation | 2.0772 × |
20772 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand seven hundred and seventy-two |
| Binary (base 2) | 101000100100100 |
| Octal (base 8) | 50444 |
| Hexadecimal (base 16) | 5124 |
| Base 3 | 1001111100 |
| As time | 20772 seconds = 5 h 46 min 12 s |
Is 20772 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20772 ÷ 2 = 10386) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (20772 ÷ 3 = 6924) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20772 ÷ 4 = 5193) | 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 (20772 ÷ 6 = 3462) | 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 | Yes (20772 ÷ 9 = 2308) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (20772 ÷ 12 = 1731) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20772 a prime number?
No. 20772 = × × 577, so it is divisible by 2.
What are the factors of 20772?
1, 2, 3, 4, 6, 9, 12, 18, 36, 577, 1154, 1731, 2308, 3462, 5193, 6924, 10386, 20772.
What is 20772 in binary?
101000100100100 (hexadecimal 5124, octal 50444).
What is the square root of 20772?
About 144.1249, exactly 6√577.
Is 20772 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 20772?
20772 is a Harshad number: divisible by its digit sum 18.