The number 10400
10400 is a composite number with 36 divisors. Its prime factorisation is × × 13. Divisors (36): 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65 … 10400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10400: a Harshad number: divisible by its digit sum 5.
- 2
10400 is composite. Its prime factorisation is
- 3
The divisors add up to 27342; without 10400 itself that is 16942, so 10400 is abundant (16942 is more than 10400). Euler's totient φ(10400) = 3840 numbers up to 10400 share no factor with it.
- 4
The digits of 10400 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 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10400 = 2^{5} \times 5^{2} \times 13 \]10400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 27342 |
| Euler totient φ(n) | 3840 |
| Square | 108160000 |
| Cube | 1124864000000 |
| Square root | 101.980390 (= 20√26) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.04 × |
10400 in other forms
| Form | Value |
|---|---|
| In words | ten thousand four hundred |
| Binary (base 2) | 10100010100000 |
| Octal (base 8) | 24240 |
| Hexadecimal (base 16) | 28A0 |
| Base 3 | 112021012 |
| As time | 10400 seconds = 2 h 53 min 20 s |
Is 10400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10400 ÷ 2 = 5200) | 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 (10400 ÷ 4 = 2600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10400 ÷ 5 = 2080) | 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 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 (10400 ÷ 8 = 1300) | 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 (10400 ÷ 10 = 1040) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | 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 10400 a prime number?
No. 10400 = × × 13, so it is divisible by 2.
What are the factors of 10400?
1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 130, 160, 200, 208, 260, 325, 400, 416, 520, 650, 800, 1040, 1300, 2080, 2600, 5200, 10400.
What is 10400 in binary?
10100010100000 (hexadecimal 28A0, octal 24240).
What is the square root of 10400?
About 101.9804, exactly 20√26.
Is 10400 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 10400?
10400 is a Harshad number: divisible by its digit sum 5.