The number 53664
53664 is a composite number with 48 divisors. Its prime factorisation is × 3 × 13 × 43. Divisors (48): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 43, 48, 52 … 53664.
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How to work it out
- 1
What is special about 53664: a Harshad number: divisible by its digit sum 24.
- 2
53664 is composite. Its prime factorisation is
- 3
The divisors add up to 155232; without 53664 itself that is 101568, so 53664 is abundant (101568 is more than 53664). Euler's totient φ(53664) = 16128 numbers up to 53664 share no factor with it.
- 4
The digits of 53664 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 53664 = 2^{5} \times 3 \times 13 \times 43 \]53664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 155232 |
| Euler totient φ(n) | 16128 |
| Square | 2879824896 |
| Cube | 154542923218944 |
| Square root | 231.654916 (= 4√3354) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 47 |
| Scientific notation | 5.3664 × |
53664 in other forms
| Form | Value |
|---|---|
| In words | fifty-three thousand six hundred and sixty-four |
| Binary (base 2) | 1101000110100000 |
| Octal (base 8) | 150640 |
| Hexadecimal (base 16) | D1A0 |
| Base 3 | 2201121120 |
| As time | 53664 seconds = 14 h 54 min 24 s |
Is 53664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (53664 ÷ 2 = 26832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (53664 ÷ 3 = 17888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (53664 ÷ 4 = 13416) | 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 (53664 ÷ 6 = 8944) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (53664 ÷ 8 = 6708) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (53664 ÷ 12 = 4472) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 53664 a prime number?
No. 53664 = × 3 × 13 × 43, so it is divisible by 2.
What are the factors of 53664?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 43, 48, 52, 78, 86, 96, 104, 129, 156, 172, 208, 258, 312, 344, 416, 516, 559, 624, 688, 1032, 1118, 1248, 1376, 1677, 2064, 2236, 3354, 4128, 4472, 6708, 8944, 13416, 17888, 26832, 53664.
What is 53664 in binary?
1101000110100000 (hexadecimal D1A0, octal 150640).
What is the square root of 53664?
About 231.6549, exactly 4√3354.
Is 53664 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 53664?
53664 is a Harshad number: divisible by its digit sum 24.