The number 87648
87648 is a composite number with 48 divisors. Its prime factorisation is × 3 × 11 × 83. Divisors (48): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66 … 87648.
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How to work it out
- 1
What is special about 87648: a Harshad number: divisible by its digit sum 33.
- 2
87648 is composite. Its prime factorisation is
- 3
The divisors add up to 254016; without 87648 itself that is 166368, so 87648 is abundant (166368 is more than 87648). Euler's totient φ(87648) = 26240 numbers up to 87648 share no factor with it.
- 4
The digits of 87648 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 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87648 = 2^{5} \times 3 \times 11 \times 83 \]87648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 254016 |
| Euler totient φ(n) | 26240 |
| Square | 7682171904 |
| Cube | 673327003041792 |
| Square root | 296.054049 (= 4√5478) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 45 |
| Scientific notation | 8.7648 × |
87648 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand six hundred and forty-eight |
| Binary (base 2) | 10101011001100000 |
| Octal (base 8) | 253140 |
| Hexadecimal (base 16) | 15660 |
| Base 3 | 11110020020 |
| As time | 87648 seconds = 24 h 20 min 48 s |
Is 87648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87648 ÷ 2 = 43824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87648 ÷ 3 = 29216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87648 ÷ 4 = 21912) | 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 (87648 ÷ 6 = 14608) | 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 (87648 ÷ 8 = 10956) | 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 (87648 ÷ 11 = 7968) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87648 ÷ 12 = 7304) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87648 a prime number?
No. 87648 = × 3 × 11 × 83, so it is divisible by 2.
What are the factors of 87648?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 83, 88, 96, 132, 166, 176, 249, 264, 332, 352, 498, 528, 664, 913, 996, 1056, 1328, 1826, 1992, 2656, 2739, 3652, 3984, 5478, 7304, 7968, 10956, 14608, 21912, 29216, 43824, 87648.
What is 87648 in binary?
10101011001100000 (hexadecimal 15660, octal 253140).
What is the square root of 87648?
About 296.0540, exactly 4√5478.
Is 87648 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 87648?
87648 is a Harshad number: divisible by its digit sum 33.