The number 13770
13770 is a composite number with 40 divisors. Its prime factorisation is 2 × × 5 × 17. Divisors (40): 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 27, 30, 34, 45, 51, 54 … 13770.
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How to work it out
- 1
What is special about 13770: a Harshad number: divisible by its digit sum 18.
- 2
13770 is composite. Its prime factorisation is
- 3
The divisors add up to 39204; without 13770 itself that is 25434, so 13770 is abundant (25434 is more than 13770). Euler's totient φ(13770) = 3456 numbers up to 13770 share no factor with it.
- 4
The digits of 13770 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 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13770 = 2 \times 3^{4} \times 5 \times 17 \]13770 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 39204 |
| Euler totient φ(n) | 3456 |
| Square | 189612900 |
| Cube | 2610969633000 |
| Square root | 117.345643 (= 9√170) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.377 × |
13770 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and seventy |
| Binary (base 2) | 11010111001010 |
| Octal (base 8) | 32712 |
| Hexadecimal (base 16) | 35CA |
| Base 3 | 200220000 |
| As time | 13770 seconds = 3 h 49 min 30 s |
Is 13770 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13770 ÷ 2 = 6885) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13770 ÷ 3 = 4590) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13770 ÷ 5 = 2754) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13770 ÷ 6 = 2295) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13770 ÷ 9 = 1530) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13770 ÷ 10 = 1377) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13770 a prime number?
No. 13770 = 2 × × 5 × 17, so it is divisible by 2.
What are the factors of 13770?
1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 27, 30, 34, 45, 51, 54, 81, 85, 90, 102, 135, 153, 162, 170, 255, 270, 306, 405, 459, 510, 765, 810, 918, 1377, 1530, 2295, 2754, 4590, 6885, 13770.
What is 13770 in binary?
11010111001010 (hexadecimal 35CA, octal 32712).
What is the square root of 13770?
About 117.3456, exactly 9√170.
Is 13770 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13770?
13770 is a Harshad number: divisible by its digit sum 18.