The number 69984
69984 is a composite number with 48 divisors. Its prime factorisation is × . Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 69984.
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How to work it out
- 1
What is special about 69984: a Harshad number: divisible by its digit sum 36.
- 2
69984 is composite. Its prime factorisation is
- 3
The divisors add up to 206640; without 69984 itself that is 136656, so 69984 is abundant (136656 is more than 69984). Euler's totient φ(69984) = 23328 numbers up to 69984 share no factor with it.
- 4
The digits of 69984 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 81 steps to reach 1.
LaTeX source of the formulas on this page
\[ 69984 = 2^{5} \times 3^{7} \]69984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 206640 |
| Euler totient φ(n) | 23328 |
| Square | 4897760256 |
| Cube | 342764853755904 |
| Square root | 264.544892 (= 108√6) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 81 |
| Scientific notation | 6.9984 × |
69984 in other forms
| Form | Value |
|---|---|
| In words | sixty-nine thousand nine hundred and eighty-four |
| Binary (base 2) | 10001000101100000 |
| Octal (base 8) | 210540 |
| Hexadecimal (base 16) | 11160 |
| Base 3 | 10120000000 |
| As time | 69984 seconds = 19 h 26 min 24 s |
Is 69984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (69984 ÷ 2 = 34992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (69984 ÷ 3 = 23328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (69984 ÷ 4 = 17496) | 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 (69984 ÷ 6 = 11664) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (69984 ÷ 8 = 8748) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (69984 ÷ 9 = 7776) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (69984 ÷ 12 = 5832) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 69984 a prime number?
No. 69984 = × , so it is divisible by 2.
What are the factors of 69984?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 729, 864, 972, 1296, 1458, 1944, 2187, 2592, 2916, 3888, 4374, 5832, 7776, 8748, 11664, 17496, 23328, 34992, 69984.
What is 69984 in binary?
10001000101100000 (hexadecimal 11160, octal 210540).
What is the square root of 69984?
About 264.5449, exactly 108√6.
Is 69984 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 69984?
69984 is a Harshad number: divisible by its digit sum 36.