The number 10104
10104 is a composite number with 16 divisors. Its prime factorisation is × 3 × 421. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 421, 842, 1263, 1684, 2526, 3368, 5052, 10104.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10104: a Harshad number: divisible by its digit sum 6.
- 2
10104 is composite. Its prime factorisation is
- 3
The divisors add up to 25320; without 10104 itself that is 15216, so 10104 is abundant (15216 is more than 10104). Euler's totient φ(10104) = 3360 numbers up to 10104 share no factor with it.
- 4
The digits of 10104 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 179 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10104 = 2^{3} \times 3 \times 421 \]10104 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 25320 |
| Euler totient φ(n) | 3360 |
| Square | 102090816 |
| Cube | 1031525604864 |
| Square root | 100.518655 (= 2√2526) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 179 |
| Scientific notation | 1.0104 × |
10104 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred and four |
| Binary (base 2) | 10011101111000 |
| Octal (base 8) | 23570 |
| Hexadecimal (base 16) | 2778 |
| Base 3 | 111212020 |
| As time | 10104 seconds = 2 h 48 min 24 s |
Is 10104 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10104 ÷ 2 = 5052) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10104 ÷ 3 = 3368) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10104 ÷ 4 = 2526) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10104 ÷ 6 = 1684) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (10104 ÷ 8 = 1263) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10104 ÷ 12 = 842) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10104 a prime number?
No. 10104 = × 3 × 421, so it is divisible by 2.
What are the factors of 10104?
1, 2, 3, 4, 6, 8, 12, 24, 421, 842, 1263, 1684, 2526, 3368, 5052, 10104.
What is 10104 in binary?
10011101111000 (hexadecimal 2778, octal 23570).
What is the square root of 10104?
About 100.5187, exactly 2√2526.
Is 10104 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 10104?
10104 is a Harshad number: divisible by its digit sum 6.