The number 2448
2448 is a composite number with 30 divisors. Its prime factorisation is × × 17. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51 … 2448.
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How to work it out
- 1
What is special about 2448: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
2448 is composite. Its prime factorisation is
- 3
The divisors add up to 7254; without 2448 itself that is 4806, so 2448 is abundant (4806 is more than 2448). Euler's totient φ(2448) = 768 numbers up to 2448 share no factor with it.
- 4
The digits of 2448 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2448 = 2^{4} \times 3^{2} \times 17 \]2448 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 7254 |
| Euler totient φ(n) | 768 |
| Square | 5992704 |
| Cube | 14670139392 |
| Square root | 49.477268 (= 12√17) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 40 |
| Scientific notation | 2.448 × |
2448 in other forms
| Form | Value |
|---|---|
| In words | two thousand four hundred and forty-eight |
| Roman numerals | MMCDXLVIII |
| Binary (base 2) | 100110010000 |
| Octal (base 8) | 4620 |
| Hexadecimal (base 16) | 990 |
| Base 3 | 10100200 |
| As time | 2448 seconds = 40 min 48 s |
Is 2448 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2448 ÷ 2 = 1224) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2448 ÷ 3 = 816) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2448 ÷ 4 = 612) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2448 ÷ 6 = 408) | 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 (2448 ÷ 8 = 306) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (2448 ÷ 9 = 272) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2448 ÷ 12 = 204) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2448 a prime number?
No. 2448 = × × 17, so it is divisible by 2.
What are the factors of 2448?
1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51, 68, 72, 102, 136, 144, 153, 204, 272, 306, 408, 612, 816, 1224, 2448.
What is 2448 in binary?
100110010000 (hexadecimal 990, octal 4620).
What is the square root of 2448?
About 49.4773, exactly 12√17.
What is 2448 in Roman numerals?
MMCDXLVIII.
Is 2448 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 2448?
2448 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.