The number 13797
13797 is a composite number with 16 divisors. Its prime factorisation is × 7 × 73. Divisors (16): 1, 3, 7, 9, 21, 27, 63, 73, 189, 219, 511, 657, 1533, 1971, 4599, 13797.
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How to work it out
- 1
What is special about 13797: a Harshad number: divisible by its digit sum 27.
- 2
13797 is composite. Its prime factorisation is
- 3
The divisors add up to 23680; without 13797 itself that is 9883, so 13797 is deficient (9883 is less than 13797). Euler's totient φ(13797) = 7776 numbers up to 13797 share no factor with it.
- 4
The digits of 13797 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13797 = 3^{3} \times 7 \times 73 \]13797 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 23680 |
| Euler totient φ(n) | 7776 |
| Square | 190357209 |
| Cube | 2626358412573 |
| Square root | 117.460632 (= 3√1533) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3797 × |
13797 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and ninety-seven |
| Binary (base 2) | 11010111100101 |
| Octal (base 8) | 32745 |
| Hexadecimal (base 16) | 35E5 |
| Base 3 | 200221000 |
| As time | 13797 seconds = 3 h 49 min 57 s |
Is 13797 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13797 ÷ 3 = 4599) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13797 ÷ 7 = 1971) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13797 ÷ 9 = 1533) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13797 a prime number?
No. 13797 = × 7 × 73, so it is divisible by 3.
What are the factors of 13797?
1, 3, 7, 9, 21, 27, 63, 73, 189, 219, 511, 657, 1533, 1971, 4599, 13797.
What is 13797 in binary?
11010111100101 (hexadecimal 35E5, octal 32745).
What is the square root of 13797?
About 117.4606, exactly 3√1533.
Is 13797 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 13797?
13797 is a Harshad number: divisible by its digit sum 27.