The number 18984
18984 is a composite number with 32 divisors. Its prime factorisation is × 3 × 7 × 113. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 113 … 18984.
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How to work it out
- 1
What is special about 18984: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
18984 is composite. Its prime factorisation is
- 3
The divisors add up to 54720; without 18984 itself that is 35736, so 18984 is abundant (35736 is more than 18984). Euler's totient φ(18984) = 5376 numbers up to 18984 share no factor with it.
- 4
The digits of 18984 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 79 steps to reach 1.
LaTeX source of the formulas on this page
\[ 18984 = 2^{3} \times 3 \times 7 \times 113 \]18984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 54720 |
| Euler totient φ(n) | 5376 |
| Square | 360392256 |
| Cube | 6841686587904 |
| Square root | 137.782437 (= 2√4746) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 79 |
| Scientific notation | 1.8984 × |
18984 in other forms
| Form | Value |
|---|---|
| In words | eighteen thousand nine hundred and eighty-four |
| Binary (base 2) | 100101000101000 |
| Octal (base 8) | 45050 |
| Hexadecimal (base 16) | 4A28 |
| Base 3 | 222001010 |
| As time | 18984 seconds = 5 h 16 min 24 s |
Is 18984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (18984 ÷ 2 = 9492) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (18984 ÷ 3 = 6328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (18984 ÷ 4 = 4746) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (18984 ÷ 6 = 3164) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (18984 ÷ 7 = 2712) | 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 | Yes (18984 ÷ 8 = 2373) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | Yes (18984 ÷ 12 = 1582) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 18984 a prime number?
No. 18984 = × 3 × 7 × 113, so it is divisible by 2.
What are the factors of 18984?
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 113, 168, 226, 339, 452, 678, 791, 904, 1356, 1582, 2373, 2712, 3164, 4746, 6328, 9492, 18984.
What is 18984 in binary?
100101000101000 (hexadecimal 4A28, octal 45050).
What is the square root of 18984?
About 137.7824, exactly 2√4746.
Is 18984 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 18984?
18984 is a happy number: repeatedly adding the squares of its digits reaches 1.