The number 10464
10464 is a composite number with 24 divisors. Its prime factorisation is × 3 × 109. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 109, 218, 327, 436 … 10464.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10464 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10464 is composite. Its prime factorisation is
- 3
The divisors add up to 27720; without 10464 itself that is 17256, so 10464 is abundant (17256 is more than 10464). Euler's totient φ(10464) = 3456 numbers up to 10464 share no factor with it.
- 4
The digits of 10464 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 148 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10464 = 2^{5} \times 3 \times 109 \]10464 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 27720 |
| Euler totient φ(n) | 3456 |
| Square | 109495296 |
| Cube | 1145758777344 |
| Square root | 102.293695 (= 4√654) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 148 |
| Scientific notation | 1.0464 × |
10464 in other forms
| Form | Value |
|---|---|
| In words | ten thousand four hundred and sixty-four |
| Binary (base 2) | 10100011100000 |
| Octal (base 8) | 24340 |
| Hexadecimal (base 16) | 28E0 |
| Base 3 | 112100120 |
| As time | 10464 seconds = 2 h 54 min 24 s |
Is 10464 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10464 ÷ 2 = 5232) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10464 ÷ 3 = 3488) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10464 ÷ 4 = 2616) | 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 (10464 ÷ 6 = 1744) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (10464 ÷ 8 = 1308) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10464 ÷ 12 = 872) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10464 a prime number?
No. 10464 = × 3 × 109, so it is divisible by 2.
What are the factors of 10464?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 109, 218, 327, 436, 654, 872, 1308, 1744, 2616, 3488, 5232, 10464.
What is 10464 in binary?
10100011100000 (hexadecimal 28E0, octal 24340).
What is the square root of 10464?
About 102.2937, exactly 4√654.
Is 10464 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 10464?
It is a composite number with 24 divisors.