The number 13152
13152 is a composite number with 24 divisors. Its prime factorisation is × 3 × 137. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 137, 274, 411, 548 … 13152.
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How to work it out
- 1
What is special about 13152: a Harshad number: divisible by its digit sum 12.
- 2
13152 is composite. Its prime factorisation is
- 3
The divisors add up to 34776; without 13152 itself that is 21624, so 13152 is abundant (21624 is more than 13152). Euler's totient φ(13152) = 4352 numbers up to 13152 share no factor with it.
- 4
The digits of 13152 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13152 = 2^{5} \times 3 \times 137 \]13152 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 34776 |
| Euler totient φ(n) | 4352 |
| Square | 172975104 |
| Cube | 2274968567808 |
| Square root | 114.682169 (= 4√822) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.3152 × |
13152 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand one hundred and fifty-two |
| Binary (base 2) | 11001101100000 |
| Octal (base 8) | 31540 |
| Hexadecimal (base 16) | 3360 |
| Base 3 | 200001010 |
| As time | 13152 seconds = 3 h 39 min 12 s |
Is 13152 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13152 ÷ 2 = 6576) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13152 ÷ 3 = 4384) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13152 ÷ 4 = 3288) | 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 (13152 ÷ 6 = 2192) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (13152 ÷ 8 = 1644) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13152 ÷ 12 = 1096) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13152 a prime number?
No. 13152 = × 3 × 137, so it is divisible by 2.
What are the factors of 13152?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 137, 274, 411, 548, 822, 1096, 1644, 2192, 3288, 4384, 6576, 13152.
What is 13152 in binary?
11001101100000 (hexadecimal 3360, octal 31540).
What is the square root of 13152?
About 114.6822, exactly 4√822.
Is 13152 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 13152?
13152 is a Harshad number: divisible by its digit sum 12.