The number 2964
2964 is a composite number with 24 divisors. Its prime factorisation is × 3 × 13 × 19. Divisors (24): 1, 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114 … 2964.
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How to work it out
- 1
2964 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
2964 is composite. Its prime factorisation is
- 3
The divisors add up to 7840; without 2964 itself that is 4876, so 2964 is abundant (4876 is more than 2964). Euler's totient φ(2964) = 864 numbers up to 2964 share no factor with it.
- 4
The digits of 2964 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2964 = 2^{2} \times 3 \times 13 \times 19 \]2964 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 7840 |
| Euler totient φ(n) | 864 |
| Square | 8785296 |
| Cube | 26039617344 |
| Square root | 54.442630 (= 2√741) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 48 |
| Scientific notation | 2.964 × |
2964 in other forms
| Form | Value |
|---|---|
| In words | two thousand nine hundred and sixty-four |
| Roman numerals | MMCMLXIV |
| Binary (base 2) | 101110010100 |
| Octal (base 8) | 5624 |
| Hexadecimal (base 16) | B94 |
| Base 3 | 11001210 |
| As time | 2964 seconds = 49 min 24 s |
Is 2964 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2964 ÷ 2 = 1482) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2964 ÷ 3 = 988) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2964 ÷ 4 = 741) | 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 (2964 ÷ 6 = 494) | 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 | No (remainder 4) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2964 ÷ 12 = 247) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2964 a prime number?
No. 2964 = × 3 × 13 × 19, so it is divisible by 2.
What are the factors of 2964?
1, 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, 1482, 2964.
What is 2964 in binary?
101110010100 (hexadecimal B94, octal 5624).
What is the square root of 2964?
About 54.4426, exactly 2√741.
What is 2964 in Roman numerals?
MMCMLXIV.
Is 2964 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 2964?
It is a composite number with 24 divisors.