The number 87984
87984 is a composite number with 60 divisors. Its prime factorisation is × × 13 × 47. Divisors (60): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 47 … 87984.
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How to work it out
- 1
What is special about 87984: a Harshad number: divisible by its digit sum 36.
- 2
87984 is composite. Its prime factorisation is
- 3
The divisors add up to 270816; without 87984 itself that is 182832, so 87984 is abundant (182832 is more than 87984). Euler's totient φ(87984) = 26496 numbers up to 87984 share no factor with it.
- 4
The digits of 87984 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 71 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87984 = 2^{4} \times 3^{2} \times 13 \times 47 \]87984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 270816 |
| Euler totient φ(n) | 26496 |
| Square | 7741184256 |
| Cube | 681100355579904 |
| Square root | 296.620970 (= 12√611) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 71 |
| Scientific notation | 8.7984 × |
87984 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand nine hundred and eighty-four |
| Binary (base 2) | 10101011110110000 |
| Octal (base 8) | 253660 |
| Hexadecimal (base 16) | 157B0 |
| Base 3 | 11110200200 |
| As time | 87984 seconds = 24 h 26 min 24 s |
Is 87984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87984 ÷ 2 = 43992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87984 ÷ 3 = 29328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87984 ÷ 4 = 21996) | 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 (87984 ÷ 6 = 14664) | 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 | Yes (87984 ÷ 8 = 10998) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (87984 ÷ 9 = 9776) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87984 ÷ 12 = 7332) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87984 a prime number?
No. 87984 = × × 13 × 47, so it is divisible by 2.
What are the factors of 87984?
1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 47, 48, 52, 72, 78, 94, 104, 117, 141, 144, 156, 188, 208, 234, 282, 312, 376, 423, 468, 564, 611, 624, 752, 846, 936, 1128, 1222, 1692, 1833, 1872, 2256, 2444, 3384, 3666, 4888, 5499, 6768, 7332, 9776, 10998, 14664, 21996, 29328, 43992, 87984.
What is 87984 in binary?
10101011110110000 (hexadecimal 157B0, octal 253660).
What is the square root of 87984?
About 296.6210, exactly 12√611.
Is 87984 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 87984?
87984 is a Harshad number: divisible by its digit sum 36.