The number 53964
53964 is a composite number with 18 divisors. Its prime factorisation is × × 1499. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 1499, 2998, 4497, 5996, 8994, 13491, 17988 … 53964.
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How to work it out
- 1
What is special about 53964: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
53964 is composite. Its prime factorisation is
- 3
The divisors add up to 136500; without 53964 itself that is 82536, so 53964 is abundant (82536 is more than 53964). Euler's totient φ(53964) = 17976 numbers up to 53964 share no factor with it.
- 4
The digits of 53964 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 78 steps to reach 1.
LaTeX source of the formulas on this page
\[ 53964 = 2^{2} \times 3^{2} \times 1499 \]53964 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 136500 |
| Euler totient φ(n) | 17976 |
| Square | 2912113296 |
| Cube | 157149281905344 |
| Square root | 232.301528 (= 6√1499) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 78 |
| Scientific notation | 5.3964 × |
53964 in other forms
| Form | Value |
|---|---|
| In words | fifty-three thousand nine hundred and sixty-four |
| Binary (base 2) | 1101001011001100 |
| Octal (base 8) | 151314 |
| Hexadecimal (base 16) | D2CC |
| Base 3 | 2202000200 |
| As time | 53964 seconds = 14 h 59 min 24 s |
Is 53964 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (53964 ÷ 2 = 26982) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (53964 ÷ 3 = 17988) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (53964 ÷ 4 = 13491) | 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 (53964 ÷ 6 = 8994) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | Yes (53964 ÷ 9 = 5996) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (53964 ÷ 12 = 4497) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 53964 a prime number?
No. 53964 = × × 1499, so it is divisible by 2.
What are the factors of 53964?
1, 2, 3, 4, 6, 9, 12, 18, 36, 1499, 2998, 4497, 5996, 8994, 13491, 17988, 26982, 53964.
What is 53964 in binary?
1101001011001100 (hexadecimal D2CC, octal 151314).
What is the square root of 53964?
About 232.3015, exactly 6√1499.
Is 53964 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 53964?
53964 is a happy number: repeatedly adding the squares of its digits reaches 1.