The number 13121
13121 is the 1561st prime number. Its only divisors are 1 and 13121.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13121: the 1561st prime number.
- 2
13121 is prime, so its only factors are 1 and 13121. It is the 1561st prime; the next prime is 13127 and the one before is 13109.
- 3
The divisors add up to 13122; without 13121 itself that is 1, so 13121 is deficient (1 is less than 13121). Euler's totient φ(13121) = 13120 numbers up to 13121 share no factor with it.
- 4
The digits of 13121 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
13121 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13122 |
| Euler totient φ(n) | 13120 |
| Square | 172160641 |
| Cube | 2258919770561 |
| Square root | 114.546934 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3121 × |
13121 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand one hundred and twenty-one |
| Binary (base 2) | 11001101000001 |
| Octal (base 8) | 31501 |
| Hexadecimal (base 16) | 3341 |
| Base 3 | 122222222 |
| As time | 13121 seconds = 3 h 38 min 41 s |
Is 13121 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 1) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 13121 a prime number?
Yes. 13121 is divisible only by 1 and itself.
What are the factors of 13121?
1, 13121.
What is 13121 in binary?
11001101000001 (hexadecimal 3341, octal 31501).
What is the square root of 13121?
About 114.5469.
Is 13121 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 13121?
13121 is the 1561st prime number.