The number 8040
8040 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 67. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 67 … 8040.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8040: a Harshad number: divisible by its digit sum 12.
- 2
8040 is composite. Its prime factorisation is
- 3
The divisors add up to 24480; without 8040 itself that is 16440, so 8040 is abundant (16440 is more than 8040). Euler's totient φ(8040) = 2112 numbers up to 8040 share no factor with it.
- 4
The digits of 8040 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 70 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8040 = 2^{3} \times 3 \times 5 \times 67 \]8040 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 24480 |
| Euler totient φ(n) | 2112 |
| Square | 64641600 |
| Cube | 519718464000 |
| Square root | 89.666047 (= 2√2010) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 70 |
| Scientific notation | 8.04 × |
8040 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and forty |
| Binary (base 2) | 1111101101000 |
| Octal (base 8) | 17550 |
| Hexadecimal (base 16) | 1F68 |
| Base 3 | 102000210 |
| As time | 8040 seconds = 2 h 14 min 0 s |
Is 8040 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8040 ÷ 2 = 4020) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8040 ÷ 3 = 2680) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8040 ÷ 4 = 2010) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (8040 ÷ 5 = 1608) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8040 ÷ 6 = 1340) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (8040 ÷ 8 = 1005) | 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 (8040 ÷ 10 = 804) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8040 ÷ 12 = 670) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8040 a prime number?
No. 8040 = × 3 × 5 × 67, so it is divisible by 2.
What are the factors of 8040?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 67, 120, 134, 201, 268, 335, 402, 536, 670, 804, 1005, 1340, 1608, 2010, 2680, 4020, 8040.
What is 8040 in binary?
1111101101000 (hexadecimal 1F68, octal 17550).
What is the square root of 8040?
About 89.6660, exactly 2√2010.
Is 8040 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 8040?
8040 is a Harshad number: divisible by its digit sum 12.