The number 7984
7984 is a composite number with 10 divisors. Its prime factorisation is × 499. Divisors (10): 1, 2, 4, 8, 16, 499, 998, 1996, 3992, 7984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
7984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
7984 is composite. Its prime factorisation is
- 3
The divisors add up to 15500; without 7984 itself that is 7516, so 7984 is deficient (7516 is less than 7984). Euler's totient φ(7984) = 3984 numbers up to 7984 share no factor with it.
- 4
The digits of 7984 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7984 = 2^{4} \times 499 \]7984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 15500 |
| Euler totient φ(n) | 3984 |
| Square | 63744256 |
| Cube | 508934139904 |
| Square root | 89.353232 (= 4√499) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 52 |
| Scientific notation | 7.984 × |
7984 in other forms
| Form | Value |
|---|---|
| In words | seven thousand nine hundred and eighty-four |
| Binary (base 2) | 1111100110000 |
| Octal (base 8) | 17460 |
| Hexadecimal (base 16) | 1F30 |
| Base 3 | 101221201 |
| As time | 7984 seconds = 2 h 13 min 4 s |
Is 7984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7984 ÷ 2 = 3992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7984 ÷ 4 = 1996) | 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 | No (remainder 4) | 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 (7984 ÷ 8 = 998) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7984 a prime number?
No. 7984 = × 499, so it is divisible by 2.
What are the factors of 7984?
1, 2, 4, 8, 16, 499, 998, 1996, 3992, 7984.
What is 7984 in binary?
1111100110000 (hexadecimal 1F30, octal 17460).
What is the square root of 7984?
About 89.3532, exactly 4√499.
Is 7984 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 7984?
It is a composite number with 10 divisors.