The number 984
984 is a composite number with 16 divisors. Its prime factorisation is × 3 × 41. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
984 is composite. Its prime factorisation is
- 3
The divisors add up to 2520; without 984 itself that is 1536, so 984 is abundant (1536 is more than 984). Euler's totient φ(984) = 320 numbers up to 984 share no factor with it.
- 4
The digits of 984 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 984 = 2^{3} \times 3 \times 41 \]984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 2520 |
| Euler totient φ(n) | 320 |
| Square | 968256 |
| Cube | 952763904 |
| Square root | 31.368774 (= 2√246) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 49 |
| Scientific notation | 9.84 × |
984 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and eighty-four |
| Roman numerals | CMLXXXIV |
| Binary (base 2) | 1111011000 |
| Octal (base 8) | 1730 |
| Hexadecimal (base 16) | 3D8 |
| Base 3 | 1100110 |
| As time | 984 seconds = 16 min 24 s |
Is 984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (984 ÷ 2 = 492) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (984 ÷ 3 = 328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (984 ÷ 4 = 246) | 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 (984 ÷ 6 = 164) | 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 | Yes (984 ÷ 8 = 123) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (984 ÷ 12 = 82) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 984 a prime number?
No. 984 = × 3 × 41, so it is divisible by 2.
What are the factors of 984?
1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984.
What is 984 in binary?
1111011000 (hexadecimal 3D8, octal 1730).
What is the square root of 984?
About 31.3688, exactly 2√246.
What is 984 in Roman numerals?
CMLXXXIV.
Is 984 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 984?
It is a composite number with 16 divisors.