The number 13472
13472 is a composite number with 12 divisors. Its prime factorisation is × 421. Divisors (12): 1, 2, 4, 8, 16, 32, 421, 842, 1684, 3368, 6736, 13472.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13472: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13472 is composite. Its prime factorisation is
- 3
The divisors add up to 26586; without 13472 itself that is 13114, so 13472 is deficient (13114 is less than 13472). Euler's totient φ(13472) = 6720 numbers up to 13472 share no factor with it.
- 4
The digits of 13472 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13472 = 2^{5} \times 421 \]13472 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 26586 |
| Euler totient φ(n) | 6720 |
| Square | 181494784 |
| Cube | 2445097730048 |
| Square root | 116.068945 (= 4√842) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3472 × |
13472 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand four hundred and seventy-two |
| Binary (base 2) | 11010010100000 |
| Octal (base 8) | 32240 |
| Hexadecimal (base 16) | 34A0 |
| Base 3 | 200110222 |
| As time | 13472 seconds = 3 h 44 min 32 s |
Is 13472 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13472 ÷ 2 = 6736) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13472 ÷ 4 = 3368) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 | Yes (13472 ÷ 8 = 1684) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13472 a prime number?
No. 13472 = × 421, so it is divisible by 2.
What are the factors of 13472?
1, 2, 4, 8, 16, 32, 421, 842, 1684, 3368, 6736, 13472.
What is 13472 in binary?
11010010100000 (hexadecimal 34A0, octal 32240).
What is the square root of 13472?
About 116.0689, exactly 4√842.
Is 13472 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 13472?
13472 is a happy number: repeatedly adding the squares of its digits reaches 1.