The number 13488
13488 is a composite number with 20 divisors. Its prime factorisation is × 3 × 281. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 281, 562, 843, 1124, 1686, 2248 … 13488.
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How to work it out
- 1
What is special about 13488: a Harshad number: divisible by its digit sum 24.
- 2
13488 is composite. Its prime factorisation is
- 3
The divisors add up to 34968; without 13488 itself that is 21480, so 13488 is abundant (21480 is more than 13488). Euler's totient φ(13488) = 4480 numbers up to 13488 share no factor with it.
- 4
The digits of 13488 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13488 = 2^{4} \times 3 \times 281 \]13488 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 34968 |
| Euler totient φ(n) | 4480 |
| Square | 181926144 |
| Cube | 2453819830272 |
| Square root | 116.137849 (= 4√843) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3488 × |
13488 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand four hundred and eighty-eight |
| Binary (base 2) | 11010010110000 |
| Octal (base 8) | 32260 |
| Hexadecimal (base 16) | 34B0 |
| Base 3 | 200111120 |
| As time | 13488 seconds = 3 h 44 min 48 s |
Is 13488 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13488 ÷ 2 = 6744) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13488 ÷ 3 = 4496) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13488 ÷ 4 = 3372) | 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 (13488 ÷ 6 = 2248) | 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 (13488 ÷ 8 = 1686) | 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 | No (remainder 8) | 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 (13488 ÷ 12 = 1124) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13488 a prime number?
No. 13488 = × 3 × 281, so it is divisible by 2.
What are the factors of 13488?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 281, 562, 843, 1124, 1686, 2248, 3372, 4496, 6744, 13488.
What is 13488 in binary?
11010010110000 (hexadecimal 34B0, octal 32260).
What is the square root of 13488?
About 116.1378, exactly 4√843.
Is 13488 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 13488?
13488 is a Harshad number: divisible by its digit sum 24.