The number 1365
1365 is a binary palindrome (10101010101). Its prime factorisation is 3 × 5 × 7 × 13. Divisors (16): 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1365: a binary palindrome (10101010101); a Harshad number: divisible by its digit sum 15.
- 2
1365 is composite. Its prime factorisation is
- 3
The divisors add up to 2688; without 1365 itself that is 1323, so 1365 is deficient (1323 is less than 1365). Euler's totient φ(1365) = 576 numbers up to 1365 share no factor with it.
- 4
The digits of 1365 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 13 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1365 = 3 \times 5 \times 7 \times 13 \]
1365 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 2688 |
| Euler totient φ(n) | 576 |
| Square | 1863225 |
| Cube | 2543302125 |
| Square root | 36.945906 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 13 |
| Scientific notation | 1.365 × |
1365 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and sixty-five |
| Roman numerals | MCCCLXV |
| Binary (base 2) | 10101010101 |
| Octal (base 8) | 2525 |
| Hexadecimal (base 16) | 555 |
| Base 3 | 1212120 |
| As time | 1365 seconds = 22 min 45 s |
Is 1365 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 (1365 ÷ 3 = 455) | 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 (1365 ÷ 5 = 273) | 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 | Yes (1365 ÷ 7 = 195) | 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 5) | 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 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 1365 a prime number?
No. 1365 = 3 × 5 × 7 × 13, so it is divisible by 3.
What are the factors of 1365?
1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365.
What is 1365 in binary?
10101010101 (hexadecimal 555, octal 2525).
What is the square root of 1365?
About 36.9459.
What is 1365 in Roman numerals?
MCCCLXV.
Is 1365 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 1365?
1365 is a binary palindrome (10101010101); a Harshad number: divisible by its digit sum 15.