The number 13188
13188 is a composite number with 24 divisors. Its prime factorisation is × 3 × 7 × 157. Divisors (24): 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 157, 314, 471, 628 … 13188.
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How to work it out
- 1
What is special about 13188: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
13188 is composite. Its prime factorisation is
- 3
The divisors add up to 35392; without 13188 itself that is 22204, so 13188 is abundant (22204 is more than 13188). Euler's totient φ(13188) = 3744 numbers up to 13188 share no factor with it.
- 4
The digits of 13188 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 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13188 = 2^{2} \times 3 \times 7 \times 157 \]13188 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 35392 |
| Euler totient φ(n) | 3744 |
| Square | 173923344 |
| Cube | 2293701060672 |
| Square root | 114.839018 (= 2√3297) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 125 |
| Scientific notation | 1.3188 × |
13188 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand one hundred and eighty-eight |
| Binary (base 2) | 11001110000100 |
| Octal (base 8) | 31604 |
| Hexadecimal (base 16) | 3384 |
| Base 3 | 200002110 |
| As time | 13188 seconds = 3 h 39 min 48 s |
Is 13188 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13188 ÷ 2 = 6594) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13188 ÷ 3 = 4396) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13188 ÷ 4 = 3297) | 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 (13188 ÷ 6 = 2198) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13188 ÷ 7 = 1884) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13188 ÷ 12 = 1099) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13188 a prime number?
No. 13188 = × 3 × 7 × 157, so it is divisible by 2.
What are the factors of 13188?
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 157, 314, 471, 628, 942, 1099, 1884, 2198, 3297, 4396, 6594, 13188.
What is 13188 in binary?
11001110000100 (hexadecimal 3384, octal 31604).
What is the square root of 13188?
About 114.8390, exactly 2√3297.
Is 13188 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 13188?
13188 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.