The number 13428
13428 is a composite number with 18 divisors. Its prime factorisation is × × 373. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 373, 746, 1119, 1492, 2238, 3357, 4476 … 13428.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13428: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
13428 is composite. Its prime factorisation is
- 3
The divisors add up to 34034; without 13428 itself that is 20606, so 13428 is abundant (20606 is more than 13428). Euler's totient φ(13428) = 4464 numbers up to 13428 share no factor with it.
- 4
The digits of 13428 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 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13428 = 2^{2} \times 3^{2} \times 373 \]13428 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 34034 |
| Euler totient φ(n) | 4464 |
| Square | 180311184 |
| Cube | 2421218578752 |
| Square root | 115.879247 (= 6√373) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 1.3428 × |
13428 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand four hundred and twenty-eight |
| Binary (base 2) | 11010001110100 |
| Octal (base 8) | 32164 |
| Hexadecimal (base 16) | 3474 |
| Base 3 | 200102100 |
| As time | 13428 seconds = 3 h 43 min 48 s |
Is 13428 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13428 ÷ 2 = 6714) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13428 ÷ 3 = 4476) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13428 ÷ 4 = 3357) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13428 ÷ 6 = 2238) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (13428 ÷ 9 = 1492) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 | Yes (13428 ÷ 12 = 1119) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13428 a prime number?
No. 13428 = × × 373, so it is divisible by 2.
What are the factors of 13428?
1, 2, 3, 4, 6, 9, 12, 18, 36, 373, 746, 1119, 1492, 2238, 3357, 4476, 6714, 13428.
What is 13428 in binary?
11010001110100 (hexadecimal 3474, octal 32164).
What is the square root of 13428?
About 115.8792, exactly 6√373.
Is 13428 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13428?
13428 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.