The number 12138
12138 is a composite number with 24 divisors. Its prime factorisation is 2 × 3 × 7 × . Divisors (24): 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 289, 357 … 12138.
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How to work it out
- 1
What is special about 12138: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
12138 is composite. Its prime factorisation is
- 3
The divisors add up to 29472; without 12138 itself that is 17334, so 12138 is abundant (17334 is more than 12138). Euler's totient φ(12138) = 3264 numbers up to 12138 share no factor with it.
- 4
The digits of 12138 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12138 = 2 \times 3 \times 7 \times 17^{2} \]12138 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 29472 |
| Euler totient φ(n) | 3264 |
| Square | 147331044 |
| Cube | 1788304212072 |
| Square root | 110.172592 (= 17√42) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 63 |
| Scientific notation | 1.2138 × |
12138 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand one hundred and thirty-eight |
| Binary (base 2) | 10111101101010 |
| Octal (base 8) | 27552 |
| Hexadecimal (base 16) | 2F6A |
| Base 3 | 121122120 |
| As time | 12138 seconds = 3 h 22 min 18 s |
Is 12138 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12138 ÷ 2 = 6069) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12138 ÷ 3 = 4046) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12138 ÷ 6 = 2023) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (12138 ÷ 7 = 1734) | 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 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12138 a prime number?
No. 12138 = 2 × 3 × 7 × , so it is divisible by 2.
What are the factors of 12138?
1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 289, 357, 578, 714, 867, 1734, 2023, 4046, 6069, 12138.
What is 12138 in binary?
10111101101010 (hexadecimal 2F6A, octal 27552).
What is the square root of 12138?
About 110.1726, exactly 17√42.
Is 12138 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 12138?
12138 is a happy number: repeatedly adding the squares of its digits reaches 1.