The number 23121
23121 is a composite number with 12 divisors. Its prime factorisation is × 7 × 367. Divisors (12): 1, 3, 7, 9, 21, 63, 367, 1101, 2569, 3303, 7707, 23121.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 23121: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
23121 is composite. Its prime factorisation is
- 3
The divisors add up to 38272; without 23121 itself that is 15151, so 23121 is deficient (15151 is less than 23121). Euler's totient φ(23121) = 13176 numbers up to 23121 share no factor with it.
- 4
The digits of 23121 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 69 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23121 = 3^{2} \times 7 \times 367 \]23121 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 38272 |
| Euler totient φ(n) | 13176 |
| Square | 534580641 |
| Cube | 12360039000561 |
| Square root | 152.055911 (= 3√2569) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 69 |
| Scientific notation | 2.3121 × |
23121 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand one hundred and twenty-one |
| Binary (base 2) | 101101001010001 |
| Octal (base 8) | 55121 |
| Hexadecimal (base 16) | 5A51 |
| Base 3 | 1011201100 |
| As time | 23121 seconds = 6 h 25 min 21 s |
Is 23121 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 (23121 ÷ 3 = 7707) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (23121 ÷ 7 = 3303) | 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 | Yes (23121 ÷ 9 = 2569) | 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 10) | 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 23121 a prime number?
No. 23121 = × 7 × 367, so it is divisible by 3.
What are the factors of 23121?
1, 3, 7, 9, 21, 63, 367, 1101, 2569, 3303, 7707, 23121.
What is 23121 in binary?
101101001010001 (hexadecimal 5A51, octal 55121).
What is the square root of 23121?
About 152.0559, exactly 3√2569.
Is 23121 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 23121?
23121 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.