The number 59964
59964 is a composite number with 24 divisors. Its prime factorisation is × 3 × 19 × 263. Divisors (24): 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228, 263, 526, 789, 1052 … 59964.
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How to work it out
- 1
What is special about 59964: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
59964 is composite. Its prime factorisation is
- 3
The divisors add up to 147840; without 59964 itself that is 87876, so 59964 is abundant (87876 is more than 59964). Euler's totient φ(59964) = 18864 numbers up to 59964 share no factor with it.
- 4
The digits of 59964 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 59964 = 2^{2} \times 3 \times 19 \times 263 \]59964 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 147840 |
| Euler totient φ(n) | 18864 |
| Square | 3595681296 |
| Cube | 215611433233344 |
| Square root | 244.875479 (= 2√14991) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 73 |
| Scientific notation | 5.9964 × |
59964 in other forms
| Form | Value |
|---|---|
| In words | fifty-nine thousand nine hundred and sixty-four |
| Binary (base 2) | 1110101000111100 |
| Octal (base 8) | 165074 |
| Hexadecimal (base 16) | EA3C |
| Base 3 | 10001020220 |
| As time | 59964 seconds = 16 h 39 min 24 s |
Is 59964 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (59964 ÷ 2 = 29982) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (59964 ÷ 3 = 19988) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (59964 ÷ 4 = 14991) | 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 (59964 ÷ 6 = 9994) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | Yes (59964 ÷ 12 = 4997) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 59964 a prime number?
No. 59964 = × 3 × 19 × 263, so it is divisible by 2.
What are the factors of 59964?
1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228, 263, 526, 789, 1052, 1578, 3156, 4997, 9994, 14991, 19988, 29982, 59964.
What is 59964 in binary?
1110101000111100 (hexadecimal EA3C, octal 165074).
What is the square root of 59964?
About 244.8755, exactly 2√14991.
Is 59964 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 59964?
59964 is a happy number: repeatedly adding the squares of its digits reaches 1.