The number 2145
2145 is a triangular number: 1 + 2 + … + 65 = 2145 and a binary palindrome (100001100001). Its prime factorisation is 3 × 5 × 11 × 13. Divisors (16): 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2145: a triangular number: 1 + 2 + … + 65 = 2145; a binary palindrome (100001100001).
- 2
2145 is composite. Its prime factorisation is
- 3
The divisors add up to 4032; without 2145 itself that is 1887, so 2145 is deficient (1887 is less than 2145). Euler's totient φ(2145) = 960 numbers up to 2145 share no factor with it.
- 4
The digits of 2145 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2145 = 3 \times 5 \times 11 \times 13 \]
2145 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 4032 |
| Euler totient φ(n) | 960 |
| Square | 4601025 |
| Cube | 9869198625 |
| Square root | 46.314145 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 76 |
| Scientific notation | 2.145 × |
2145 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and forty-five |
| Roman numerals | MMCXLV |
| Binary (base 2) | 100001100001 |
| Octal (base 8) | 4141 |
| Hexadecimal (base 16) | 861 |
| Base 3 | 2221110 |
| As time | 2145 seconds = 35 min 45 s |
Is 2145 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2145 ÷ 3 = 715) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2145 ÷ 5 = 429) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 1) | 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 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (2145 ÷ 11 = 195) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2145 a prime number?
No. 2145 = 3 × 5 × 11 × 13, so it is divisible by 3.
What are the factors of 2145?
1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145.
What is 2145 in binary?
100001100001 (hexadecimal 861, octal 4141).
What is the square root of 2145?
About 46.3141.
What is 2145 in Roman numerals?
MMCXLV.
Is 2145 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 2145?
2145 is a triangular number: 1 + 2 + … + 65 = 2145; a binary palindrome (100001100001).