The number 4188
4188 is a composite number with 12 divisors. Its prime factorisation is × 3 × 349. Divisors (12): 1, 2, 3, 4, 6, 12, 349, 698, 1047, 1396, 2094, 4188.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
4188 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
4188 is composite. Its prime factorisation is
- 3
The divisors add up to 9800; without 4188 itself that is 5612, so 4188 is abundant (5612 is more than 4188). Euler's totient φ(4188) = 1392 numbers up to 4188 share no factor with it.
- 4
The digits of 4188 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 126 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4188 = 2^{2} \times 3 \times 349 \]4188 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 9800 |
| Euler totient φ(n) | 1392 |
| Square | 17539344 |
| Cube | 73454772672 |
| Square root | 64.714759 (= 2√1047) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 126 |
| Scientific notation | 4.188 × |
4188 in other forms
| Form | Value |
|---|---|
| In words | four thousand one hundred and eighty-eight |
| Binary (base 2) | 1000001011100 |
| Octal (base 8) | 10134 |
| Hexadecimal (base 16) | 105C |
| Base 3 | 12202010 |
| As time | 4188 seconds = 1 h 9 min 48 s |
Is 4188 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4188 ÷ 2 = 2094) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (4188 ÷ 3 = 1396) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4188 ÷ 4 = 1047) | 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 (4188 ÷ 6 = 698) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (4188 ÷ 12 = 349) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4188 a prime number?
No. 4188 = × 3 × 349, so it is divisible by 2.
What are the factors of 4188?
1, 2, 3, 4, 6, 12, 349, 698, 1047, 1396, 2094, 4188.
What is 4188 in binary?
1000001011100 (hexadecimal 105C, octal 10134).
What is the square root of 4188?
About 64.7148, exactly 2√1047.
Is 4188 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 4188?
It is a composite number with 12 divisors.