The number 47984
47984 is a composite number with 10 divisors. Its prime factorisation is × 2999. Divisors (10): 1, 2, 4, 8, 16, 2999, 5998, 11996, 23992, 47984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 47984: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
47984 is composite. Its prime factorisation is
- 3
The divisors add up to 93000; without 47984 itself that is 45016, so 47984 is deficient (45016 is less than 47984). Euler's totient φ(47984) = 23984 numbers up to 47984 share no factor with it.
- 4
The digits of 47984 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47984 = 2^{4} \times 2999 \]47984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 93000 |
| Euler totient φ(n) | 23984 |
| Square | 2302464256 |
| Cube | 110481444859904 |
| Square root | 219.052505 (= 4√2999) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.7984 × |
47984 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand nine hundred and eighty-four |
| Binary (base 2) | 1011101101110000 |
| Octal (base 8) | 135560 |
| Hexadecimal (base 16) | BB70 |
| Base 3 | 2102211012 |
| As time | 47984 seconds = 13 h 19 min 44 s |
Is 47984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47984 ÷ 2 = 23992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47984 ÷ 4 = 11996) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (47984 ÷ 8 = 5998) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47984 a prime number?
No. 47984 = × 2999, so it is divisible by 2.
What are the factors of 47984?
1, 2, 4, 8, 16, 2999, 5998, 11996, 23992, 47984.
What is 47984 in binary?
1011101101110000 (hexadecimal BB70, octal 135560).
What is the square root of 47984?
About 219.0525, exactly 4√2999.
Is 47984 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 47984?
47984 is a happy number: repeatedly adding the squares of its digits reaches 1.