The number 46752
46752 is a composite number with 24 divisors. Its prime factorisation is × 3 × 487. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 487, 974, 1461, 1948 … 46752.
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How to work it out
- 1
What is special about 46752: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.
- 2
46752 is composite. Its prime factorisation is
- 3
The divisors add up to 122976; without 46752 itself that is 76224, so 46752 is abundant (76224 is more than 46752). Euler's totient φ(46752) = 15552 numbers up to 46752 share no factor with it.
- 4
The digits of 46752 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 46752 = 2^{5} \times 3 \times 487 \]46752 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 122976 |
| Euler totient φ(n) | 15552 |
| Square | 2185749504 |
| Cube | 102188160811008 |
| Square root | 216.222108 (= 4√2922) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 101 |
| Scientific notation | 4.6752 × |
46752 in other forms
| Form | Value |
|---|---|
| In words | forty-six thousand seven hundred and fifty-two |
| Binary (base 2) | 1011011010100000 |
| Octal (base 8) | 133240 |
| Hexadecimal (base 16) | B6A0 |
| Base 3 | 2101010120 |
| As time | 46752 seconds = 12 h 59 min 12 s |
Is 46752 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (46752 ÷ 2 = 23376) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (46752 ÷ 3 = 15584) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (46752 ÷ 4 = 11688) | 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 (46752 ÷ 6 = 7792) | 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 (46752 ÷ 8 = 5844) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (46752 ÷ 12 = 3896) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 46752 a prime number?
No. 46752 = × 3 × 487, so it is divisible by 2.
What are the factors of 46752?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 487, 974, 1461, 1948, 2922, 3896, 5844, 7792, 11688, 15584, 23376, 46752.
What is 46752 in binary?
1011011010100000 (hexadecimal B6A0, octal 133240).
What is the square root of 46752?
About 216.2221, exactly 4√2922.
Is 46752 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 46752?
46752 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.