The number 2064
2064 is a composite number with 20 divisors. Its prime factorisation is × 3 × 43. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 43, 48, 86, 129, 172, 258, 344 … 2064.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2064: a Harshad number: divisible by its digit sum 12.
- 2
2064 is composite. Its prime factorisation is
- 3
The divisors add up to 5456; without 2064 itself that is 3392, so 2064 is abundant (3392 is more than 2064). Euler's totient φ(2064) = 672 numbers up to 2064 share no factor with it.
- 4
The digits of 2064 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 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2064 = 2^{4} \times 3 \times 43 \]2064 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 5456 |
| Euler totient φ(n) | 672 |
| Square | 4260096 |
| Cube | 8792838144 |
| Square root | 45.431267 (= 4√129) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 125 |
| Scientific notation | 2.064 × |
2064 in other forms
| Form | Value |
|---|---|
| In words | two thousand and sixty-four |
| Roman numerals | MMLXIV |
| Binary (base 2) | 100000010000 |
| Octal (base 8) | 4020 |
| Hexadecimal (base 16) | 810 |
| Base 3 | 2211110 |
| As time | 2064 seconds = 34 min 24 s |
Is 2064 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2064 ÷ 2 = 1032) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2064 ÷ 3 = 688) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2064 ÷ 4 = 516) | 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 (2064 ÷ 6 = 344) | 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 (2064 ÷ 8 = 258) | 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 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2064 ÷ 12 = 172) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2064 a prime number?
No. 2064 = × 3 × 43, so it is divisible by 2.
What are the factors of 2064?
1, 2, 3, 4, 6, 8, 12, 16, 24, 43, 48, 86, 129, 172, 258, 344, 516, 688, 1032, 2064.
What is 2064 in binary?
100000010000 (hexadecimal 810, octal 4020).
What is the square root of 2064?
About 45.4313, exactly 4√129.
What is 2064 in Roman numerals?
MMLXIV.
Is 2064 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 2064?
2064 is a Harshad number: divisible by its digit sum 12.