The number 61824
61824 is a composite number with 64 divisors. Its prime factorisation is × 3 × 7 × 23. Divisors (64): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 32, 42 … 61824.
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How to work it out
- 1
What is special about 61824: a Harshad number: divisible by its digit sum 21.
- 2
61824 is composite. Its prime factorisation is
- 3
The divisors add up to 195840; without 61824 itself that is 134016, so 61824 is abundant (134016 is more than 61824). Euler's totient φ(61824) = 16896 numbers up to 61824 share no factor with it.
- 4
The digits of 61824 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 61824 = 2^{7} \times 3 \times 7 \times 23 \]61824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 195840 |
| Euler totient φ(n) | 16896 |
| Square | 3822206976 |
| Cube | 236304124084224 |
| Square root | 248.644324 (= 8√966) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 29 |
| Scientific notation | 6.1824 × |
61824 in other forms
| Form | Value |
|---|---|
| In words | sixty-one thousand eight hundred and twenty-four |
| Binary (base 2) | 1111000110000000 |
| Octal (base 8) | 170600 |
| Hexadecimal (base 16) | F180 |
| Base 3 | 10010210210 |
| As time | 61824 seconds = 17 h 10 min 24 s |
Is 61824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (61824 ÷ 2 = 30912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (61824 ÷ 3 = 20608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (61824 ÷ 4 = 15456) | 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 (61824 ÷ 6 = 10304) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (61824 ÷ 7 = 8832) | 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 (61824 ÷ 8 = 7728) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 (61824 ÷ 12 = 5152) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61824 a prime number?
No. 61824 = × 3 × 7 × 23, so it is divisible by 2.
What are the factors of 61824?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 32, 42, 46, 48, 56, 64, 69, 84, 92, 96, 112, 128, 138, 161, 168, 184, 192, 224, 276, 322, 336, 368, 384, 448, 483, 552, 644, 672, 736, 896, 966, 1104, 1288, 1344, 1472, 1932, 2208, 2576, 2688, 2944, 3864, 4416, 5152, 7728, 8832, 10304, 15456, 20608, 30912, 61824.
What is 61824 in binary?
1111000110000000 (hexadecimal F180, octal 170600).
What is the square root of 61824?
About 248.6443, exactly 8√966.
Is 61824 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 61824?
61824 is a Harshad number: divisible by its digit sum 21.