The number 15264
15264 is a composite number with 36 divisors. Its prime factorisation is × × 53. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 53, 72 … 15264.
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How to work it out
- 1
What is special about 15264: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
15264 is composite. Its prime factorisation is
- 3
The divisors add up to 44226; without 15264 itself that is 28962, so 15264 is abundant (28962 is more than 15264). Euler's totient φ(15264) = 4992 numbers up to 15264 share no factor with it.
- 4
The digits of 15264 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 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 15264 = 2^{5} \times 3^{2} \times 53 \]15264 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 44226 |
| Euler totient φ(n) | 4992 |
| Square | 232989696 |
| Cube | 3556354719744 |
| Square root | 123.547562 (= 12√106) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 40 |
| Scientific notation | 1.5264 × |
15264 in other forms
| Form | Value |
|---|---|
| In words | fifteen thousand two hundred and sixty-four |
| Binary (base 2) | 11101110100000 |
| Octal (base 8) | 35640 |
| Hexadecimal (base 16) | 3BA0 |
| Base 3 | 202221100 |
| As time | 15264 seconds = 4 h 14 min 24 s |
Is 15264 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (15264 ÷ 2 = 7632) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (15264 ÷ 3 = 5088) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (15264 ÷ 4 = 3816) | 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 | Yes (15264 ÷ 6 = 2544) | 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 (15264 ÷ 8 = 1908) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (15264 ÷ 9 = 1696) | 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 | Yes (15264 ÷ 12 = 1272) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 15264 a prime number?
No. 15264 = × × 53, so it is divisible by 2.
What are the factors of 15264?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 53, 72, 96, 106, 144, 159, 212, 288, 318, 424, 477, 636, 848, 954, 1272, 1696, 1908, 2544, 3816, 5088, 7632, 15264.
What is 15264 in binary?
11101110100000 (hexadecimal 3BA0, octal 35640).
What is the square root of 15264?
About 123.5476, exactly 12√106.
Is 15264 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 15264?
15264 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.