The number 12993
12993 is a composite number with 8 divisors. Its prime factorisation is 3 × 61 × 71. Divisors (8): 1, 3, 61, 71, 183, 213, 4331, 12993.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12993: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
12993 is composite. Its prime factorisation is
- 3
The divisors add up to 17856; without 12993 itself that is 4863, so 12993 is deficient (4863 is less than 12993). Euler's totient φ(12993) = 8400 numbers up to 12993 share no factor with it.
- 4
The digits of 12993 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12993 = 3 \times 61 \times 71 \]
12993 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 17856 |
| Euler totient φ(n) | 8400 |
| Square | 168818049 |
| Cube | 2193452910657 |
| Square root | 113.986841 |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.2993 × |
12993 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand nine hundred and ninety-three |
| Binary (base 2) | 11001011000001 |
| Octal (base 8) | 31301 |
| Hexadecimal (base 16) | 32C1 |
| Base 3 | 122211020 |
| As time | 12993 seconds = 3 h 36 min 33 s |
Is 12993 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 (12993 ÷ 3 = 4331) | 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 3) | 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 | No (remainder 1) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | 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 12993 a prime number?
No. 12993 = 3 × 61 × 71, so it is divisible by 3.
What are the factors of 12993?
1, 3, 61, 71, 183, 213, 4331, 12993.
What is 12993 in binary?
11001011000001 (hexadecimal 32C1, octal 31301).
What is the square root of 12993?
About 113.9868.
Is 12993 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 12993?
12993 is a happy number: repeatedly adding the squares of its digits reaches 1.