The number 59520
59520 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 31. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32 … 59520.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
59520 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
59520 is composite. Its prime factorisation is
- 3
The divisors add up to 195840; without 59520 itself that is 136320, so 59520 is abundant (136320 is more than 59520). Euler's totient φ(59520) = 15360 numbers up to 59520 share no factor with it.
- 4
The digits of 59520 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 59520 = 2^{7} \times 3 \times 5 \times 31 \]59520 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 195840 |
| Euler totient φ(n) | 15360 |
| Square | 3542630400 |
| Cube | 210857361408000 |
| Square root | 243.967211 (= 8√930) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 42 |
| Scientific notation | 5.952 × |
59520 in other forms
| Form | Value |
|---|---|
| In words | fifty-nine thousand five hundred and twenty |
| Binary (base 2) | 1110100010000000 |
| Octal (base 8) | 164200 |
| Hexadecimal (base 16) | E880 |
| Base 3 | 10000122110 |
| As time | 59520 seconds = 16 h 32 min 0 s |
Is 59520 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (59520 ÷ 2 = 29760) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (59520 ÷ 3 = 19840) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (59520 ÷ 4 = 14880) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (59520 ÷ 5 = 11904) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (59520 ÷ 6 = 9920) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (59520 ÷ 8 = 7440) | 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 | Yes (59520 ÷ 10 = 5952) | 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 (59520 ÷ 12 = 4960) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 59520 a prime number?
No. 59520 = × 3 × 5 × 31, so it is divisible by 2.
What are the factors of 59520?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32, 40, 48, 60, 62, 64, 80, 93, 96, 120, 124, 128, 155, 160, 186, 192, 240, 248, 310, 320, 372, 384, 465, 480, 496, 620, 640, 744, 930, 960, 992, 1240, 1488, 1860, 1920, 1984, 2480, 2976, 3720, 3968, 4960, 5952, 7440, 9920, 11904, 14880, 19840, 29760, 59520.
What is 59520 in binary?
1110100010000000 (hexadecimal E880, octal 164200).
What is the square root of 59520?
About 243.9672, exactly 8√930.
Is 59520 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 59520?
It is a composite number with 64 divisors.