The number 51624
51624 is a composite number with 32 divisors. Its prime factorisation is × × 239. Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216 … 51624.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 51624: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
51624 is composite. Its prime factorisation is
- 3
The divisors add up to 144000; without 51624 itself that is 92376, so 51624 is abundant (92376 is more than 51624). Euler's totient φ(51624) = 17136 numbers up to 51624 share no factor with it.
- 4
The digits of 51624 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 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 51624 = 2^{3} \times 3^{3} \times 239 \]51624 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 144000 |
| Euler totient φ(n) | 17136 |
| Square | 2665037376 |
| Cube | 137579889498624 |
| Square root | 227.209155 (= 6√1434) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 26 |
| Scientific notation | 5.1624 × |
51624 in other forms
| Form | Value |
|---|---|
| In words | fifty-one thousand six hundred and twenty-four |
| Binary (base 2) | 1100100110101000 |
| Octal (base 8) | 144650 |
| Hexadecimal (base 16) | C9A8 |
| Base 3 | 2121211000 |
| As time | 51624 seconds = 14 h 20 min 24 s |
Is 51624 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (51624 ÷ 2 = 25812) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (51624 ÷ 3 = 17208) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (51624 ÷ 4 = 12906) | 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 (51624 ÷ 6 = 8604) | 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 (51624 ÷ 8 = 6453) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (51624 ÷ 9 = 5736) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (51624 ÷ 12 = 4302) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 51624 a prime number?
No. 51624 = × × 239, so it is divisible by 2.
What are the factors of 51624?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216, 239, 478, 717, 956, 1434, 1912, 2151, 2868, 4302, 5736, 6453, 8604, 12906, 17208, 25812, 51624.
What is 51624 in binary?
1100100110101000 (hexadecimal C9A8, octal 144650).
What is the square root of 51624?
About 227.2092, exactly 6√1434.
Is 51624 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 51624?
51624 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.