The number 61632
61632 is a composite number with 42 divisors. Its prime factorisation is × × 107. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 61632.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 61632: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
61632 is composite. Its prime factorisation is
- 3
The divisors add up to 178308; without 61632 itself that is 116676, so 61632 is abundant (116676 is more than 61632). Euler's totient φ(61632) = 20352 numbers up to 61632 share no factor with it.
- 4
The digits of 61632 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 55 steps to reach 1.
LaTeX source of the formulas on this page
\[ 61632 = 2^{6} \times 3^{2} \times 107 \]61632 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 178308 |
| Euler totient φ(n) | 20352 |
| Square | 3798503424 |
| Cube | 234109363027968 |
| Square root | 248.257930 (= 24√107) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 55 |
| Scientific notation | 6.1632 × |
61632 in other forms
| Form | Value |
|---|---|
| In words | sixty-one thousand six hundred and thirty-two |
| Binary (base 2) | 1111000011000000 |
| Octal (base 8) | 170300 |
| Hexadecimal (base 16) | F0C0 |
| Base 3 | 10010112200 |
| As time | 61632 seconds = 17 h 7 min 12 s |
Is 61632 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (61632 ÷ 2 = 30816) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (61632 ÷ 3 = 20544) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (61632 ÷ 4 = 15408) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (61632 ÷ 6 = 10272) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (61632 ÷ 8 = 7704) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (61632 ÷ 9 = 6848) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (61632 ÷ 12 = 5136) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61632 a prime number?
No. 61632 = × × 107, so it is divisible by 2.
What are the factors of 61632?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 107, 144, 192, 214, 288, 321, 428, 576, 642, 856, 963, 1284, 1712, 1926, 2568, 3424, 3852, 5136, 6848, 7704, 10272, 15408, 20544, 30816, 61632.
What is 61632 in binary?
1111000011000000 (hexadecimal F0C0, octal 170300).
What is the square root of 61632?
About 248.2579, exactly 24√107.
Is 61632 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 61632?
61632 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.