The number 13020
13020 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 7 × 31. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 31 … 13020.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13020: a Harshad number: divisible by its digit sum 6.
- 2
13020 is composite. Its prime factorisation is
- 3
The divisors add up to 43008; without 13020 itself that is 29988, so 13020 is abundant (29988 is more than 13020). Euler's totient φ(13020) = 2880 numbers up to 13020 share no factor with it.
- 4
The digits of 13020 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13020 = 2^{2} \times 3 \times 5 \times 7 \times 31 \]13020 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 43008 |
| Euler totient φ(n) | 2880 |
| Square | 169520400 |
| Cube | 2207155608000 |
| Square root | 114.105215 (= 2√3255) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 76 |
| Scientific notation | 1.302 × |
13020 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and twenty |
| Binary (base 2) | 11001011011100 |
| Octal (base 8) | 31334 |
| Hexadecimal (base 16) | 32DC |
| Base 3 | 122212020 |
| As time | 13020 seconds = 3 h 37 min 0 s |
Is 13020 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13020 ÷ 2 = 6510) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13020 ÷ 3 = 4340) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13020 ÷ 4 = 3255) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13020 ÷ 5 = 2604) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13020 ÷ 6 = 2170) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13020 ÷ 7 = 1860) | 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 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13020 ÷ 10 = 1302) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13020 ÷ 12 = 1085) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13020 a prime number?
No. 13020 = × 3 × 5 × 7 × 31, so it is divisible by 2.
What are the factors of 13020?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 31, 35, 42, 60, 62, 70, 84, 93, 105, 124, 140, 155, 186, 210, 217, 310, 372, 420, 434, 465, 620, 651, 868, 930, 1085, 1302, 1860, 2170, 2604, 3255, 4340, 6510, 13020.
What is 13020 in binary?
11001011011100 (hexadecimal 32DC, octal 31334).
What is the square root of 13020?
About 114.1052, exactly 2√3255.
Is 13020 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 13020?
13020 is a Harshad number: divisible by its digit sum 6.