The number 40752
40752 is a composite number with 30 divisors. Its prime factorisation is × × 283. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 283 … 40752.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40752: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
40752 is composite. Its prime factorisation is
- 3
The divisors add up to 114452; without 40752 itself that is 73700, so 40752 is abundant (73700 is more than 40752). Euler's totient φ(40752) = 13536 numbers up to 40752 share no factor with it.
- 4
The digits of 40752 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40752 = 2^{4} \times 3^{2} \times 283 \]40752 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 114452 |
| Euler totient φ(n) | 13536 |
| Square | 1660725504 |
| Cube | 67677885739008 |
| Square root | 201.871246 (= 12√283) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 36 |
| Scientific notation | 4.0752 × |
40752 in other forms
| Form | Value |
|---|---|
| In words | forty thousand seven hundred and fifty-two |
| Binary (base 2) | 1001111100110000 |
| Octal (base 8) | 117460 |
| Hexadecimal (base 16) | 9F30 |
| Base 3 | 2001220100 |
| As time | 40752 seconds = 11 h 19 min 12 s |
Is 40752 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40752 ÷ 2 = 20376) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40752 ÷ 3 = 13584) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40752 ÷ 4 = 10188) | 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 (40752 ÷ 6 = 6792) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (40752 ÷ 8 = 5094) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (40752 ÷ 9 = 4528) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (40752 ÷ 12 = 3396) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40752 a prime number?
No. 40752 = × × 283, so it is divisible by 2.
What are the factors of 40752?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 283, 566, 849, 1132, 1698, 2264, 2547, 3396, 4528, 5094, 6792, 10188, 13584, 20376, 40752.
What is 40752 in binary?
1001111100110000 (hexadecimal 9F30, octal 117460).
What is the square root of 40752?
About 201.8712, exactly 12√283.
Is 40752 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 40752?
40752 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.