The number 97632
97632 is a composite number with 48 divisors. Its prime factorisation is × × 113. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 97632.
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How to work it out
- 1
What is special about 97632: a Harshad number: divisible by its digit sum 27.
- 2
97632 is composite. Its prime factorisation is
- 3
The divisors add up to 287280; without 97632 itself that is 189648, so 97632 is abundant (189648 is more than 97632). Euler's totient φ(97632) = 32256 numbers up to 97632 share no factor with it.
- 4
The digits of 97632 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 159 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97632 = 2^{5} \times 3^{3} \times 113 \]97632 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 287280 |
| Euler totient φ(n) | 32256 |
| Square | 9532007424 |
| Cube | 930628948819968 |
| Square root | 312.461198 (= 12√678) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 159 |
| Scientific notation | 9.7632 × |
97632 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand six hundred and thirty-two |
| Binary (base 2) | 10111110101100000 |
| Octal (base 8) | 276540 |
| Hexadecimal (base 16) | 17D60 |
| Base 3 | 11221221000 |
| As time | 97632 seconds = 27 h 7 min 12 s |
Is 97632 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97632 ÷ 2 = 48816) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97632 ÷ 3 = 32544) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97632 ÷ 4 = 24408) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (97632 ÷ 6 = 16272) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (97632 ÷ 8 = 12204) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (97632 ÷ 9 = 10848) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (97632 ÷ 12 = 8136) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97632 a prime number?
No. 97632 = × × 113, so it is divisible by 2.
What are the factors of 97632?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 113, 144, 216, 226, 288, 339, 432, 452, 678, 864, 904, 1017, 1356, 1808, 2034, 2712, 3051, 3616, 4068, 5424, 6102, 8136, 10848, 12204, 16272, 24408, 32544, 48816, 97632.
What is 97632 in binary?
10111110101100000 (hexadecimal 17D60, octal 276540).
What is the square root of 97632?
About 312.4612, exactly 12√678.
Is 97632 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 97632?
97632 is a Harshad number: divisible by its digit sum 27.