The number 264
264 is a composite number with 16 divisors. Its prime factorisation is × 3 × 11. Divisors (16): 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 264: a Harshad number: divisible by its digit sum 12.
- 2
264 is composite. Its prime factorisation is
- 3
The divisors add up to 720; without 264 itself that is 456, so 264 is abundant (456 is more than 264). Euler's totient φ(264) = 80 numbers up to 264 share no factor with it.
- 4
The digits of 264 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 264 = 2^{3} \times 3 \times 11 \]264 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 720 |
| Euler totient φ(n) | 80 |
| Square | 69696 |
| Cube | 18399744 |
| Square root | 16.248077 (= 2√66) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 29 |
| Scientific notation | 2.64 × |
264 in other forms
| Form | Value |
|---|---|
| In words | two hundred and sixty-four |
| Roman numerals | CCLXIV |
| Binary (base 2) | 100001000 |
| Octal (base 8) | 410 |
| Hexadecimal (base 16) | 108 |
| Base 3 | 100210 |
| As time | 264 seconds = 4 min 24 s |
Is 264 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (264 ÷ 2 = 132) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (264 ÷ 3 = 88) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (264 ÷ 4 = 66) | 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 (264 ÷ 6 = 44) | 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 (264 ÷ 8 = 33) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | Yes (264 ÷ 11 = 24) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (264 ÷ 12 = 22) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 264 a prime number?
No. 264 = × 3 × 11, so it is divisible by 2.
What are the factors of 264?
1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264.
What is 264 in binary?
100001000 (hexadecimal 108, octal 410).
What is the square root of 264?
About 16.2481, exactly 2√66.
What is 264 in Roman numerals?
CCLXIV.
Is 264 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 264?
264 is a Harshad number: divisible by its digit sum 12.