The number 13037
13037 is the 1553rd prime number. Its only divisors are 1 and 13037.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13037: the 1553rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13037 is prime, so its only factors are 1 and 13037. It is the 1553rd prime; the next prime is 13043 and the one before is 13033.
- 3
The divisors add up to 13038; without 13037 itself that is 1, so 13037 is deficient (1 is less than 13037). Euler's totient φ(13037) = 13036 numbers up to 13037 share no factor with it.
- 4
The digits of 13037 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
13037 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13038 |
| Euler totient φ(n) | 13036 |
| Square | 169963369 |
| Cube | 2215812441653 |
| Square root | 114.179683 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.3037 × |
13037 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and thirty-seven |
| Binary (base 2) | 11001011101101 |
| Octal (base 8) | 31355 |
| Hexadecimal (base 16) | 32ED |
| Base 3 | 122212212 |
| As time | 13037 seconds = 3 h 37 min 17 s |
Is 13037 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 | No (remainder 2) | 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 5) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13037 a prime number?
Yes. 13037 is divisible only by 1 and itself.
What are the factors of 13037?
1, 13037.
What is 13037 in binary?
11001011101101 (hexadecimal 32ED, octal 31355).
What is the square root of 13037?
About 114.1797.
Is 13037 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 13037?
13037 is the 1553rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.