The number 13752
13752 is a composite number with 24 divisors. Its prime factorisation is × × 191. Divisors (24): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 191, 382, 573, 764 … 13752.
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How to work it out
- 1
What is special about 13752: a Harshad number: divisible by its digit sum 18.
- 2
13752 is composite. Its prime factorisation is
- 3
The divisors add up to 37440; without 13752 itself that is 23688, so 13752 is abundant (23688 is more than 13752). Euler's totient φ(13752) = 4560 numbers up to 13752 share no factor with it.
- 4
The digits of 13752 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 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13752 = 2^{3} \times 3^{2} \times 191 \]13752 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 37440 |
| Euler totient φ(n) | 4560 |
| Square | 189117504 |
| Cube | 2600743915008 |
| Square root | 117.268922 (= 6√382) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3752 × |
13752 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and fifty-two |
| Binary (base 2) | 11010110111000 |
| Octal (base 8) | 32670 |
| Hexadecimal (base 16) | 35B8 |
| Base 3 | 200212100 |
| As time | 13752 seconds = 3 h 49 min 12 s |
Is 13752 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13752 ÷ 2 = 6876) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13752 ÷ 3 = 4584) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13752 ÷ 4 = 3438) | 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 | Yes (13752 ÷ 6 = 2292) | 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 (13752 ÷ 8 = 1719) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13752 ÷ 9 = 1528) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13752 ÷ 12 = 1146) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13752 a prime number?
No. 13752 = × × 191, so it is divisible by 2.
What are the factors of 13752?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 191, 382, 573, 764, 1146, 1528, 1719, 2292, 3438, 4584, 6876, 13752.
What is 13752 in binary?
11010110111000 (hexadecimal 35B8, octal 32670).
What is the square root of 13752?
About 117.2689, exactly 6√382.
Is 13752 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13752?
13752 is a Harshad number: divisible by its digit sum 18.