The number 63504
63504 is a perfect square (252²). Its prime factorisation is × × . Divisors (75): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28 … 63504.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 63504: a perfect square (252²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
63504 is composite. Its prime factorisation is
- 3
The divisors add up to 213807; without 63504 itself that is 150303, so 63504 is abundant (150303 is more than 63504). Euler's totient φ(63504) = 18144 numbers up to 63504 share no factor with it.
- 4
The digits of 63504 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 148 steps to reach 1.
LaTeX source of the formulas on this page
\[ 63504 = 2^{4} \times 3^{4} \times 7^{2} \]63504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 75 |
| Sum of divisors | 213807 |
| Euler totient φ(n) | 18144 |
| Square | 4032758016 |
| Cube | 256096265048064 |
| Square root | 252 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 148 |
| Scientific notation | 6.3504 × |
| Perfect power |
63504 in other forms
| Form | Value |
|---|---|
| In words | sixty-three thousand five hundred and four |
| Binary (base 2) | 1111100000010000 |
| Octal (base 8) | 174020 |
| Hexadecimal (base 16) | F810 |
| Base 3 | 10020010000 |
| As time | 63504 seconds = 17 h 38 min 24 s |
Is 63504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (63504 ÷ 2 = 31752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (63504 ÷ 3 = 21168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (63504 ÷ 4 = 15876) | 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 (63504 ÷ 6 = 10584) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (63504 ÷ 7 = 9072) | 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 (63504 ÷ 8 = 7938) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (63504 ÷ 9 = 7056) | 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 (63504 ÷ 12 = 5292) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 63504 a prime number?
No. 63504 = × × , so it is divisible by 2.
What are the factors of 63504?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 49, 54, 56, 63, 72, 81, 84, 98, 108, 112, 126, 144, 147, 162, 168, 189, 196, 216, 252, 294, 324, 336, 378, 392, 432, 441, 504, 567, 588, 648, 756, 784, 882, 1008, 1134, 1176, 1296, 1323, 1512, 1764, 2268, 2352, 2646, 3024, 3528, 3969, 4536, 5292, 7056, 7938, 9072, 10584, 15876, 21168, 31752, 63504.
What is 63504 in binary?
1111100000010000 (hexadecimal F810, octal 174020).
What is the square root of 63504?
252, because 252 × 252 = 63504.
Is 63504 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 63504?
63504 is a perfect square (252²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.