The number 21264
21264 is a composite number with 20 divisors. Its prime factorisation is × 3 × 443. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 443, 886, 1329, 1772, 2658, 3544 … 21264.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
21264 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
21264 is composite. Its prime factorisation is
- 3
The divisors add up to 55056; without 21264 itself that is 33792, so 21264 is abundant (33792 is more than 21264). Euler's totient φ(21264) = 7072 numbers up to 21264 share no factor with it.
- 4
The digits of 21264 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 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21264 = 2^{4} \times 3 \times 443 \]21264 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 55056 |
| Euler totient φ(n) | 7072 |
| Square | 452157696 |
| Cube | 9614681247744 |
| Square root | 145.821809 (= 4√1329) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.1264 × |
21264 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand two hundred and sixty-four |
| Binary (base 2) | 101001100010000 |
| Octal (base 8) | 51420 |
| Hexadecimal (base 16) | 5310 |
| Base 3 | 1002011120 |
| As time | 21264 seconds = 5 h 54 min 24 s |
Is 21264 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21264 ÷ 2 = 10632) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21264 ÷ 3 = 7088) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21264 ÷ 4 = 5316) | 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 (21264 ÷ 6 = 3544) | 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 (21264 ÷ 8 = 2658) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21264 ÷ 12 = 1772) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21264 a prime number?
No. 21264 = × 3 × 443, so it is divisible by 2.
What are the factors of 21264?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 443, 886, 1329, 1772, 2658, 3544, 5316, 7088, 10632, 21264.
What is 21264 in binary?
101001100010000 (hexadecimal 5310, octal 51420).
What is the square root of 21264?
About 145.8218, exactly 4√1329.
Is 21264 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 21264?
It is a composite number with 20 divisors.