The number 13780
13780 is a composite number with 24 divisors. Its prime factorisation is × 5 × 13 × 53. Divisors (24): 1, 2, 4, 5, 10, 13, 20, 26, 52, 53, 65, 106, 130, 212, 260, 265 … 13780.
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How to work it out
- 1
13780 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13780 is composite. Its prime factorisation is
- 3
The divisors add up to 31752; without 13780 itself that is 17972, so 13780 is abundant (17972 is more than 13780). Euler's totient φ(13780) = 4992 numbers up to 13780 share no factor with it.
- 4
The digits of 13780 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13780 = 2^{2} \times 5 \times 13 \times 53 \]13780 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 31752 |
| Euler totient φ(n) | 4992 |
| Square | 189888400 |
| Cube | 2616662152000 |
| Square root | 117.388245 (= 2√3445) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.378 × |
13780 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and eighty |
| Binary (base 2) | 11010111010100 |
| Octal (base 8) | 32724 |
| Hexadecimal (base 16) | 35D4 |
| Base 3 | 200220101 |
| As time | 13780 seconds = 3 h 49 min 40 s |
Is 13780 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13780 ÷ 2 = 6890) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13780 ÷ 4 = 3445) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13780 ÷ 5 = 2756) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13780 ÷ 10 = 1378) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13780 a prime number?
No. 13780 = × 5 × 13 × 53, so it is divisible by 2.
What are the factors of 13780?
1, 2, 4, 5, 10, 13, 20, 26, 52, 53, 65, 106, 130, 212, 260, 265, 530, 689, 1060, 1378, 2756, 3445, 6890, 13780.
What is 13780 in binary?
11010111010100 (hexadecimal 35D4, octal 32724).
What is the square root of 13780?
About 117.3882, exactly 2√3445.
Is 13780 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 13780?
It is a composite number with 24 divisors.