The number 10040
10040 is a composite number with 16 divisors. Its prime factorisation is × 5 × 251. Divisors (16): 1, 2, 4, 5, 8, 10, 20, 40, 251, 502, 1004, 1255, 2008, 2510, 5020, 10040.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10040: a Harshad number: divisible by its digit sum 5.
- 2
10040 is composite. Its prime factorisation is
- 3
The divisors add up to 22680; without 10040 itself that is 12640, so 10040 is abundant (12640 is more than 10040). Euler's totient φ(10040) = 4000 numbers up to 10040 share no factor with it.
- 4
The digits of 10040 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 91 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10040 = 2^{3} \times 5 \times 251 \]10040 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 22680 |
| Euler totient φ(n) | 4000 |
| Square | 100801600 |
| Cube | 1012048064000 |
| Square root | 100.199800 (= 2√2510) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 91 |
| Scientific notation | 1.004 × |
10040 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and forty |
| Binary (base 2) | 10011100111000 |
| Octal (base 8) | 23470 |
| Hexadecimal (base 16) | 2738 |
| Base 3 | 111202212 |
| As time | 10040 seconds = 2 h 47 min 20 s |
Is 10040 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10040 ÷ 2 = 5020) | 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 (10040 ÷ 4 = 2510) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10040 ÷ 5 = 2008) | 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 | No (remainder 2) | 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 (10040 ÷ 8 = 1255) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10040 ÷ 10 = 1004) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10040 a prime number?
No. 10040 = × 5 × 251, so it is divisible by 2.
What are the factors of 10040?
1, 2, 4, 5, 8, 10, 20, 40, 251, 502, 1004, 1255, 2008, 2510, 5020, 10040.
What is 10040 in binary?
10011100111000 (hexadecimal 2738, octal 23470).
What is the square root of 10040?
About 100.1998, exactly 2√2510.
Is 10040 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 10040?
10040 is a Harshad number: divisible by its digit sum 5.