The number 13724
13724 is a composite number with 12 divisors. Its prime factorisation is × 47 × 73. Divisors (12): 1, 2, 4, 47, 73, 94, 146, 188, 292, 3431, 6862, 13724.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13724: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13724 is composite. Its prime factorisation is
- 3
The divisors add up to 24864; without 13724 itself that is 11140, so 13724 is deficient (11140 is less than 13724). Euler's totient φ(13724) = 6624 numbers up to 13724 share no factor with it.
- 4
The digits of 13724 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 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13724 = 2^{2} \times 47 \times 73 \]13724 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 24864 |
| Euler totient φ(n) | 6624 |
| Square | 188348176 |
| Cube | 2584890367424 |
| Square root | 117.149477 (= 2√3431) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 120 |
| Scientific notation | 1.3724 × |
13724 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and twenty-four |
| Binary (base 2) | 11010110011100 |
| Octal (base 8) | 32634 |
| Hexadecimal (base 16) | 359C |
| Base 3 | 200211022 |
| As time | 13724 seconds = 3 h 48 min 44 s |
Is 13724 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13724 ÷ 2 = 6862) | 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 (13724 ÷ 4 = 3431) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | 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 | No (remainder 4) | 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 4) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13724 a prime number?
No. 13724 = × 47 × 73, so it is divisible by 2.
What are the factors of 13724?
1, 2, 4, 47, 73, 94, 146, 188, 292, 3431, 6862, 13724.
What is 13724 in binary?
11010110011100 (hexadecimal 359C, octal 32634).
What is the square root of 13724?
About 117.1495, exactly 2√3431.
Is 13724 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 13724?
13724 is a happy number: repeatedly adding the squares of its digits reaches 1.