The number 53988
53988 is a composite number with 24 divisors. Its prime factorisation is × 3 × 11 × 409. Divisors (24): 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132, 409, 818, 1227, 1636 … 53988.
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How to work it out
- 1
What is special about 53988: a Harshad number: divisible by its digit sum 33.
- 2
53988 is composite. Its prime factorisation is
- 3
The divisors add up to 137760; without 53988 itself that is 83772, so 53988 is abundant (83772 is more than 53988). Euler's totient φ(53988) = 16320 numbers up to 53988 share no factor with it.
- 4
The digits of 53988 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 184 steps to reach 1.
LaTeX source of the formulas on this page
\[ 53988 = 2^{2} \times 3 \times 11 \times 409 \]53988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 137760 |
| Euler totient φ(n) | 16320 |
| Square | 2914704144 |
| Cube | 157359047326272 |
| Square root | 232.353179 (= 2√13497) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 184 |
| Scientific notation | 5.3988 × |
53988 in other forms
| Form | Value |
|---|---|
| In words | fifty-three thousand nine hundred and eighty-eight |
| Binary (base 2) | 1101001011100100 |
| Octal (base 8) | 151344 |
| Hexadecimal (base 16) | D2E4 |
| Base 3 | 2202001120 |
| As time | 53988 seconds = 14 h 59 min 48 s |
Is 53988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (53988 ÷ 2 = 26994) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (53988 ÷ 3 = 17996) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (53988 ÷ 4 = 13497) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (53988 ÷ 6 = 8998) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (53988 ÷ 11 = 4908) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (53988 ÷ 12 = 4499) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 53988 a prime number?
No. 53988 = × 3 × 11 × 409, so it is divisible by 2.
What are the factors of 53988?
1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132, 409, 818, 1227, 1636, 2454, 4499, 4908, 8998, 13497, 17996, 26994, 53988.
What is 53988 in binary?
1101001011100100 (hexadecimal D2E4, octal 151344).
What is the square root of 53988?
About 232.3532, exactly 2√13497.
Is 53988 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 53988?
53988 is a Harshad number: divisible by its digit sum 33.