The number 15624
15624 is a composite number with 48 divisors. Its prime factorisation is × × 7 × 31. Divisors (48): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 31, 36 … 15624.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 15624: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
15624 is composite. Its prime factorisation is
- 3
The divisors add up to 49920; without 15624 itself that is 34296, so 15624 is abundant (34296 is more than 15624). Euler's totient φ(15624) = 4320 numbers up to 15624 share no factor with it.
- 4
The digits of 15624 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
\[ 15624 = 2^{3} \times 3^{2} \times 7 \times 31 \]15624 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 49920 |
| Euler totient φ(n) | 4320 |
| Square | 244109376 |
| Cube | 3813964890624 |
| Square root | 124.996000 (= 6√434) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 40 |
| Scientific notation | 1.5624 × |
15624 in other forms
| Form | Value |
|---|---|
| In words | fifteen thousand six hundred and twenty-four |
| Binary (base 2) | 11110100001000 |
| Octal (base 8) | 36410 |
| Hexadecimal (base 16) | 3D08 |
| Base 3 | 210102200 |
| As time | 15624 seconds = 4 h 20 min 24 s |
Is 15624 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (15624 ÷ 2 = 7812) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (15624 ÷ 3 = 5208) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (15624 ÷ 4 = 3906) | 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 (15624 ÷ 6 = 2604) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (15624 ÷ 7 = 2232) | 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 (15624 ÷ 8 = 1953) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (15624 ÷ 9 = 1736) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (15624 ÷ 12 = 1302) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 15624 a prime number?
No. 15624 = × × 7 × 31, so it is divisible by 2.
What are the factors of 15624?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 31, 36, 42, 56, 62, 63, 72, 84, 93, 124, 126, 168, 186, 217, 248, 252, 279, 372, 434, 504, 558, 651, 744, 868, 1116, 1302, 1736, 1953, 2232, 2604, 3906, 5208, 7812, 15624.
What is 15624 in binary?
11110100001000 (hexadecimal 3D08, octal 36410).
What is the square root of 15624?
About 124.9960, exactly 6√434.
Is 15624 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 15624?
15624 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.