The number 40788
40788 is a composite number with 36 divisors. Its prime factorisation is × × 11 × 103. Divisors (36): 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 103 … 40788.
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How to work it out
- 1
What is special about 40788: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
40788 is composite. Its prime factorisation is
- 3
The divisors add up to 113568; without 40788 itself that is 72780, so 40788 is abundant (72780 is more than 40788). Euler's totient φ(40788) = 12240 numbers up to 40788 share no factor with it.
- 4
The digits of 40788 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 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40788 = 2^{2} \times 3^{2} \times 11 \times 103 \]40788 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 113568 |
| Euler totient φ(n) | 12240 |
| Square | 1663660944 |
| Cube | 67857402583872 |
| Square root | 201.960392 (= 6√1133) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 62 |
| Scientific notation | 4.0788 × |
40788 in other forms
| Form | Value |
|---|---|
| In words | forty thousand seven hundred and eighty-eight |
| Binary (base 2) | 1001111101010100 |
| Octal (base 8) | 117524 |
| Hexadecimal (base 16) | 9F54 |
| Base 3 | 2001221200 |
| As time | 40788 seconds = 11 h 19 min 48 s |
Is 40788 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40788 ÷ 2 = 20394) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40788 ÷ 3 = 13596) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40788 ÷ 4 = 10197) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (40788 ÷ 6 = 6798) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (40788 ÷ 9 = 4532) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (40788 ÷ 11 = 3708) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (40788 ÷ 12 = 3399) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40788 a prime number?
No. 40788 = × × 11 × 103, so it is divisible by 2.
What are the factors of 40788?
1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 103, 132, 198, 206, 309, 396, 412, 618, 927, 1133, 1236, 1854, 2266, 3399, 3708, 4532, 6798, 10197, 13596, 20394, 40788.
What is 40788 in binary?
1001111101010100 (hexadecimal 9F54, octal 117524).
What is the square root of 40788?
About 201.9604, exactly 6√1133.
Is 40788 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 40788?
40788 is a happy number: repeatedly adding the squares of its digits reaches 1.