The number 13952
13952 is a composite number with 16 divisors. Its prime factorisation is × 109. Divisors (16): 1, 2, 4, 8, 16, 32, 64, 109, 128, 218, 436, 872, 1744, 3488, 6976, 13952.
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How to work it out
- 1
13952 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13952 is composite. Its prime factorisation is
- 3
The divisors add up to 28050; without 13952 itself that is 14098, so 13952 is abundant (14098 is more than 13952). Euler's totient φ(13952) = 6912 numbers up to 13952 share no factor with it.
- 4
The digits of 13952 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13952 = 2^{7} \times 109 \]13952 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 28050 |
| Euler totient φ(n) | 6912 |
| Square | 194658304 |
| Cube | 2715872657408 |
| Square root | 118.118584 (= 8√218) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 120 |
| Scientific notation | 1.3952 × |
13952 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and fifty-two |
| Binary (base 2) | 11011010000000 |
| Octal (base 8) | 33200 |
| Hexadecimal (base 16) | 3680 |
| Base 3 | 201010202 |
| As time | 13952 seconds = 3 h 52 min 32 s |
Is 13952 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13952 ÷ 2 = 6976) | 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 (13952 ÷ 4 = 3488) | 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 1) | 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 (13952 ÷ 8 = 1744) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 4) | 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 13952 a prime number?
No. 13952 = × 109, so it is divisible by 2.
What are the factors of 13952?
1, 2, 4, 8, 16, 32, 64, 109, 128, 218, 436, 872, 1744, 3488, 6976, 13952.
What is 13952 in binary?
11011010000000 (hexadecimal 3680, octal 33200).
What is the square root of 13952?
About 118.1186, exactly 8√218.
Is 13952 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 13952?
It is a composite number with 16 divisors.