The number 7164
7164 is a composite number with 18 divisors. Its prime factorisation is × × 199. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 199, 398, 597, 796, 1194, 1791, 2388 … 7164.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7164: a Harshad number: divisible by its digit sum 18.
- 2
7164 is composite. Its prime factorisation is
- 3
The divisors add up to 18200; without 7164 itself that is 11036, so 7164 is abundant (11036 is more than 7164). Euler's totient φ(7164) = 2376 numbers up to 7164 share no factor with it.
- 4
The digits of 7164 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 101 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7164 = 2^{2} \times 3^{2} \times 199 \]7164 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 18200 |
| Euler totient φ(n) | 2376 |
| Square | 51322896 |
| Cube | 367677226944 |
| Square root | 84.640416 (= 6√199) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 101 |
| Scientific notation | 7.164 × |
7164 in other forms
| Form | Value |
|---|---|
| In words | seven thousand one hundred and sixty-four |
| Binary (base 2) | 1101111111100 |
| Octal (base 8) | 15774 |
| Hexadecimal (base 16) | 1BFC |
| Base 3 | 100211100 |
| As time | 7164 seconds = 1 h 59 min 24 s |
Is 7164 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7164 ÷ 2 = 3582) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7164 ÷ 3 = 2388) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7164 ÷ 4 = 1791) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7164 ÷ 6 = 1194) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | Yes (7164 ÷ 9 = 796) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7164 ÷ 12 = 597) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7164 a prime number?
No. 7164 = × × 199, so it is divisible by 2.
What are the factors of 7164?
1, 2, 3, 4, 6, 9, 12, 18, 36, 199, 398, 597, 796, 1194, 1791, 2388, 3582, 7164.
What is 7164 in binary?
1101111111100 (hexadecimal 1BFC, octal 15774).
What is the square root of 7164?
About 84.6404, exactly 6√199.
Is 7164 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 7164?
7164 is a Harshad number: divisible by its digit sum 18.