The number 59040
59040 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 41. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 59040.
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How to work it out
- 1
What is special about 59040: a Harshad number: divisible by its digit sum 18.
- 2
59040 is composite. Its prime factorisation is
- 3
The divisors add up to 206388; without 59040 itself that is 147348, so 59040 is abundant (147348 is more than 59040). Euler's totient φ(59040) = 15360 numbers up to 59040 share no factor with it.
- 4
The digits of 59040 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 59040 = 2^{5} \times 3^{2} \times 5 \times 41 \]59040 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 206388 |
| Euler totient φ(n) | 15360 |
| Square | 3485721600 |
| Cube | 205797003264000 |
| Square root | 242.981481 (= 12√410) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 5.904 × |
59040 in other forms
| Form | Value |
|---|---|
| In words | fifty-nine thousand and forty |
| Binary (base 2) | 1110011010100000 |
| Octal (base 8) | 163240 |
| Hexadecimal (base 16) | E6A0 |
| Base 3 | 2222222200 |
| As time | 59040 seconds = 16 h 24 min 0 s |
Is 59040 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (59040 ÷ 2 = 29520) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (59040 ÷ 3 = 19680) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (59040 ÷ 4 = 14760) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (59040 ÷ 5 = 11808) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (59040 ÷ 6 = 9840) | 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 (59040 ÷ 8 = 7380) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (59040 ÷ 9 = 6560) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (59040 ÷ 10 = 5904) | 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 | Yes (59040 ÷ 12 = 4920) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 59040 a prime number?
No. 59040 = × × 5 × 41, so it is divisible by 2.
What are the factors of 59040?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 41, 45, 48, 60, 72, 80, 82, 90, 96, 120, 123, 144, 160, 164, 180, 205, 240, 246, 288, 328, 360, 369, 410, 480, 492, 615, 656, 720, 738, 820, 984, 1230, 1312, 1440, 1476, 1640, 1845, 1968, 2460, 2952, 3280, 3690, 3936, 4920, 5904, 6560, 7380, 9840, 11808, 14760, 19680, 29520, 59040.
What is 59040 in binary?
1110011010100000 (hexadecimal E6A0, octal 163240).
What is the square root of 59040?
About 242.9815, exactly 12√410.
Is 59040 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 59040?
59040 is a Harshad number: divisible by its digit sum 18.