The number 47952
47952 is a composite number with 50 divisors. Its prime factorisation is × × 37. Divisors (50): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 37, 48, 54 … 47952.
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How to work it out
- 1
What is special about 47952: a Harshad number: divisible by its digit sum 27.
- 2
47952 is composite. Its prime factorisation is
- 3
The divisors add up to 142538; without 47952 itself that is 94586, so 47952 is abundant (94586 is more than 47952). Euler's totient φ(47952) = 15552 numbers up to 47952 share no factor with it.
- 4
The digits of 47952 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47952 = 2^{4} \times 3^{4} \times 37 \]47952 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 50 |
| Sum of divisors | 142538 |
| Euler totient φ(n) | 15552 |
| Square | 2299394304 |
| Cube | 110260555665408 |
| Square root | 218.979451 (= 36√37) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.7952 × |
47952 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand nine hundred and fifty-two |
| Binary (base 2) | 1011101101010000 |
| Octal (base 8) | 135520 |
| Hexadecimal (base 16) | BB50 |
| Base 3 | 2102210000 |
| As time | 47952 seconds = 13 h 19 min 12 s |
Is 47952 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47952 ÷ 2 = 23976) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47952 ÷ 3 = 15984) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47952 ÷ 4 = 11988) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (47952 ÷ 6 = 7992) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (47952 ÷ 8 = 5994) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (47952 ÷ 9 = 5328) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (47952 ÷ 12 = 3996) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47952 a prime number?
No. 47952 = × × 37, so it is divisible by 2.
What are the factors of 47952?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 37, 48, 54, 72, 74, 81, 108, 111, 144, 148, 162, 216, 222, 296, 324, 333, 432, 444, 592, 648, 666, 888, 999, 1296, 1332, 1776, 1998, 2664, 2997, 3996, 5328, 5994, 7992, 11988, 15984, 23976, 47952.
What is 47952 in binary?
1011101101010000 (hexadecimal BB50, octal 135520).
What is the square root of 47952?
About 218.9795, exactly 36√37.
Is 47952 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 47952?
47952 is a Harshad number: divisible by its digit sum 27.