The number 10037
10037 is a twin prime (10037 and 10039 are both prime) and the 1232nd prime number. Its only divisors are 1 and 10037.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10037: a twin prime (10037 and 10039 are both prime); the 1232nd prime number.
- 2
10037 is prime, so its only factors are 1 and 10037. It is the 1232nd prime; the next prime is 10039 and the one before is 10009.
- 3
The divisors add up to 10038; without 10037 itself that is 1, so 10037 is deficient (1 is less than 10037). Euler's totient φ(10037) = 10036 numbers up to 10037 share no factor with it.
- 4
The digits of 10037 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
10037 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 10038 |
| Euler totient φ(n) | 10036 |
| Square | 100741369 |
| Cube | 1011141120653 |
| Square root | 100.184829 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 135 |
| Scientific notation | 1.0037 × |
10037 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and thirty-seven |
| Binary (base 2) | 10011100110101 |
| Octal (base 8) | 23465 |
| Hexadecimal (base 16) | 2735 |
| Base 3 | 111202202 |
| As time | 10037 seconds = 2 h 47 min 17 s |
Is 10037 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 6) | 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 2) | 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 5) | 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 10037 a prime number?
Yes. 10037 is divisible only by 1 and itself.
What are the factors of 10037?
1, 10037.
What is 10037 in binary?
10011100110101 (hexadecimal 2735, octal 23465).
What is the square root of 10037?
About 100.1848.
Is 10037 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 10037?
10037 is a twin prime (10037 and 10039 are both prime); the 1232nd prime number.