The number 2400
2400 is a composite number with 36 divisors. Its prime factorisation is × 3 × . Divisors (36): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32 … 2400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2400: a Harshad number: divisible by its digit sum 6.
- 2
2400 is composite. Its prime factorisation is
- 3
The divisors add up to 7812; without 2400 itself that is 5412, so 2400 is abundant (5412 is more than 2400). Euler's totient φ(2400) = 640 numbers up to 2400 share no factor with it.
- 4
The digits of 2400 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 19 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2400 = 2^{5} \times 3 \times 5^{2} \]2400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 7812 |
| Euler totient φ(n) | 640 |
| Square | 5760000 |
| Cube | 13824000000 |
| Square root | 48.989795 (= 20√6) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 19 |
| Scientific notation | 2.4 × |
2400 in other forms
| Form | Value |
|---|---|
| In words | two thousand four hundred |
| Roman numerals | MMCD |
| Binary (base 2) | 100101100000 |
| Octal (base 8) | 4540 |
| Hexadecimal (base 16) | 960 |
| Base 3 | 10021220 |
| As time | 2400 seconds = 40 min 0 s |
Is 2400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2400 ÷ 2 = 1200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2400 ÷ 3 = 800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2400 ÷ 4 = 600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2400 ÷ 5 = 480) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2400 ÷ 6 = 400) | 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 (2400 ÷ 8 = 300) | 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 | Yes (2400 ÷ 10 = 240) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2400 ÷ 12 = 200) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2400 a prime number?
No. 2400 = × 3 × , so it is divisible by 2.
What are the factors of 2400?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400.
What is 2400 in binary?
100101100000 (hexadecimal 960, octal 4540).
What is the square root of 2400?
About 48.9898, exactly 20√6.
What is 2400 in Roman numerals?
MMCD.
Is 2400 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 2400?
2400 is a Harshad number: divisible by its digit sum 6.