The number 2024
2024 is a composite number with 16 divisors. Its prime factorisation is × 11 × 23. Divisors (16): 1, 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, 1012, 2024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2024: a Harshad number: divisible by its digit sum 8.
- 2
2024 is composite. Its prime factorisation is
- 3
The divisors add up to 4320; without 2024 itself that is 2296, so 2024 is abundant (2296 is more than 2024). Euler's totient φ(2024) = 880 numbers up to 2024 share no factor with it.
- 4
The digits of 2024 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2024 = 2^{3} \times 11 \times 23 \]2024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 4320 |
| Euler totient φ(n) | 880 |
| Square | 4096576 |
| Cube | 8291469824 |
| Square root | 44.988888 (= 2√506) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 112 |
| Scientific notation | 2.024 × |
2024 in other forms
| Form | Value |
|---|---|
| In words | two thousand and twenty-four |
| Roman numerals | MMXXIV |
| Binary (base 2) | 11111101000 |
| Octal (base 8) | 3750 |
| Hexadecimal (base 16) | 7E8 |
| Base 3 | 2202222 |
| As time | 2024 seconds = 33 min 44 s |
Is 2024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2024 ÷ 2 = 1012) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2024 ÷ 4 = 506) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (2024 ÷ 8 = 253) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 (2024 ÷ 11 = 184) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2024 a prime number?
No. 2024 = × 11 × 23, so it is divisible by 2.
What are the factors of 2024?
1, 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, 1012, 2024.
What is 2024 in binary?
11111101000 (hexadecimal 7E8, octal 3750).
What is the square root of 2024?
About 44.9889, exactly 2√506.
What is 2024 in Roman numerals?
MMXXIV.
Is 2024 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 2024?
2024 is a Harshad number: divisible by its digit sum 8.