The number 13122
13122 is a composite number with 18 divisors. Its prime factorisation is 2 × . Divisors (18): 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458, 2187, 4374 … 13122.
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How to work it out
- 1
What is special about 13122: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
13122 is composite. Its prime factorisation is
- 3
The divisors add up to 29523; without 13122 itself that is 16401, so 13122 is abundant (16401 is more than 13122). Euler's totient φ(13122) = 4374 numbers up to 13122 share no factor with it.
- 4
The digits of 13122 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 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13122 = 2 \times 3^{8} \]13122 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 29523 |
| Euler totient φ(n) | 4374 |
| Square | 172186884 |
| Cube | 2259436291848 |
| Square root | 114.551299 (= 81√2) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 76 |
| Scientific notation | 1.3122 × |
13122 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand one hundred and twenty-two |
| Binary (base 2) | 11001101000010 |
| Octal (base 8) | 31502 |
| Hexadecimal (base 16) | 3342 |
| Base 3 | 200000000 |
| As time | 13122 seconds = 3 h 38 min 42 s |
Is 13122 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13122 ÷ 2 = 6561) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13122 ÷ 3 = 4374) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 | Yes (13122 ÷ 6 = 2187) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13122 ÷ 9 = 1458) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13122 a prime number?
No. 13122 = 2 × , so it is divisible by 2.
What are the factors of 13122?
1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458, 2187, 4374, 6561, 13122.
What is 13122 in binary?
11001101000010 (hexadecimal 3342, octal 31502).
What is the square root of 13122?
About 114.5513, exactly 81√2.
Is 13122 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 13122?
13122 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.