The number 40080
40080 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 167. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 40080.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40080: a Harshad number: divisible by its digit sum 12.
- 2
40080 is composite. Its prime factorisation is
- 3
The divisors add up to 124992; without 40080 itself that is 84912, so 40080 is abundant (84912 is more than 40080). Euler's totient φ(40080) = 10624 numbers up to 40080 share no factor with it.
- 4
The digits of 40080 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40080 = 2^{4} \times 3 \times 5 \times 167 \]40080 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 124992 |
| Euler totient φ(n) | 10624 |
| Square | 1606406400 |
| Cube | 64384768512000 |
| Square root | 200.199900 (= 4√2505) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 93 |
| Scientific notation | 4.008 × |
40080 in other forms
| Form | Value |
|---|---|
| In words | forty thousand and eighty |
| Binary (base 2) | 1001110010010000 |
| Octal (base 8) | 116220 |
| Hexadecimal (base 16) | 9C90 |
| Base 3 | 2000222110 |
| As time | 40080 seconds = 11 h 8 min 0 s |
Is 40080 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40080 ÷ 2 = 20040) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40080 ÷ 3 = 13360) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40080 ÷ 4 = 10020) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (40080 ÷ 5 = 8016) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (40080 ÷ 6 = 6680) | 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 (40080 ÷ 8 = 5010) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (40080 ÷ 10 = 4008) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (40080 ÷ 12 = 3340) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40080 a prime number?
No. 40080 = × 3 × 5 × 167, so it is divisible by 2.
What are the factors of 40080?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 167, 240, 334, 501, 668, 835, 1002, 1336, 1670, 2004, 2505, 2672, 3340, 4008, 5010, 6680, 8016, 10020, 13360, 20040, 40080.
What is 40080 in binary?
1001110010010000 (hexadecimal 9C90, octal 116220).
What is the square root of 40080?
About 200.1999, exactly 4√2505.
Is 40080 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 40080?
40080 is a Harshad number: divisible by its digit sum 12.