The number 61504
61504 is a perfect square (248²). Its prime factorisation is × . Divisors (21): 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 961, 992, 1922, 1984 … 61504.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 61504: a perfect square (248²); a Harshad number: divisible by its digit sum 16.
- 2
61504 is composite. Its prime factorisation is
- 3
The divisors add up to 126111; without 61504 itself that is 64607, so 61504 is abundant (64607 is more than 61504). Euler's totient φ(61504) = 29760 numbers up to 61504 share no factor with it.
- 4
The digits of 61504 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 55 steps to reach 1.
LaTeX source of the formulas on this page
\[ 61504 = 2^{6} \times 31^{2} \]61504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 21 |
| Sum of divisors | 126111 |
| Euler totient φ(n) | 29760 |
| Square | 3782742016 |
| Cube | 232653764952064 |
| Square root | 248 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 55 |
| Scientific notation | 6.1504 × |
| Perfect power |
61504 in other forms
| Form | Value |
|---|---|
| In words | sixty-one thousand five hundred and four |
| Binary (base 2) | 1111000001000000 |
| Octal (base 8) | 170100 |
| Hexadecimal (base 16) | F040 |
| Base 3 | 10010100221 |
| As time | 61504 seconds = 17 h 5 min 4 s |
Is 61504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (61504 ÷ 2 = 30752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (61504 ÷ 4 = 15376) | 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 | No (remainder 4) | 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 (61504 ÷ 8 = 7688) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61504 a prime number?
No. 61504 = × , so it is divisible by 2.
What are the factors of 61504?
1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 961, 992, 1922, 1984, 3844, 7688, 15376, 30752, 61504.
What is 61504 in binary?
1111000001000000 (hexadecimal F040, octal 170100).
What is the square root of 61504?
248, because 248 × 248 = 61504.
Is 61504 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 61504?
61504 is a perfect square (248²); a Harshad number: divisible by its digit sum 16.