The number 40040
40040 is a composite number with 64 divisors. Its prime factorisation is × 5 × 7 × 11 × 13. Divisors (64): 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 20, 22, 26, 28, 35, 40 … 40040.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40040: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.
- 2
40040 is composite. Its prime factorisation is
- 3
The divisors add up to 120960; without 40040 itself that is 80920, so 40040 is abundant (80920 is more than 40040). Euler's totient φ(40040) = 11520 numbers up to 40040 share no factor with it.
- 4
The digits of 40040 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 31 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40040 = 2^{3} \times 5 \times 7 \times 11 \times 13 \]40040 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 120960 |
| Euler totient φ(n) | 11520 |
| Square | 1603201600 |
| Cube | 64192192064000 |
| Square root | 200.099975 (= 2√10010) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 31 |
| Scientific notation | 4.004 × |
40040 in other forms
| Form | Value |
|---|---|
| In words | forty thousand and forty |
| Binary (base 2) | 1001110001101000 |
| Octal (base 8) | 116150 |
| Hexadecimal (base 16) | 9C68 |
| Base 3 | 2000220222 |
| As time | 40040 seconds = 11 h 7 min 20 s |
Is 40040 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40040 ÷ 2 = 20020) | 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 (40040 ÷ 4 = 10010) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (40040 ÷ 5 = 8008) | 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 | Yes (40040 ÷ 7 = 5720) | 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 (40040 ÷ 8 = 5005) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (40040 ÷ 10 = 4004) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (40040 ÷ 11 = 3640) | 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 40040 a prime number?
No. 40040 = × 5 × 7 × 11 × 13, so it is divisible by 2.
What are the factors of 40040?
1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 20, 22, 26, 28, 35, 40, 44, 52, 55, 56, 65, 70, 77, 88, 91, 104, 110, 130, 140, 143, 154, 182, 220, 260, 280, 286, 308, 364, 385, 440, 455, 520, 572, 616, 715, 728, 770, 910, 1001, 1144, 1430, 1540, 1820, 2002, 2860, 3080, 3640, 4004, 5005, 5720, 8008, 10010, 20020, 40040.
What is 40040 in binary?
1001110001101000 (hexadecimal 9C68, octal 116150).
What is the square root of 40040?
About 200.1000, exactly 2√10010.
Is 40040 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 40040?
40040 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 8.