The number 97884
97884 is a composite number with 18 divisors. Its prime factorisation is × × 2719. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 2719, 5438, 8157, 10876, 16314, 24471, 32628 … 97884.
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How to work it out
- 1
What is special about 97884: a Harshad number: divisible by its digit sum 36.
- 2
97884 is composite. Its prime factorisation is
- 3
The divisors add up to 247520; without 97884 itself that is 149636, so 97884 is abundant (149636 is more than 97884). Euler's totient φ(97884) = 32616 numbers up to 97884 share no factor with it.
- 4
The digits of 97884 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 115 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97884 = 2^{2} \times 3^{2} \times 2719 \]97884 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 247520 |
| Euler totient φ(n) | 32616 |
| Square | 9581277456 |
| Cube | 937853762503104 |
| Square root | 312.864188 (= 6√2719) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 115 |
| Scientific notation | 9.7884 × |
97884 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand eight hundred and eighty-four |
| Binary (base 2) | 10111111001011100 |
| Octal (base 8) | 277134 |
| Hexadecimal (base 16) | 17E5C |
| Base 3 | 11222021100 |
| As time | 97884 seconds = 27 h 11 min 24 s |
Is 97884 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97884 ÷ 2 = 48942) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97884 ÷ 3 = 32628) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97884 ÷ 4 = 24471) | 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 (97884 ÷ 6 = 16314) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (97884 ÷ 9 = 10876) | 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 (97884 ÷ 12 = 8157) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97884 a prime number?
No. 97884 = × × 2719, so it is divisible by 2.
What are the factors of 97884?
1, 2, 3, 4, 6, 9, 12, 18, 36, 2719, 5438, 8157, 10876, 16314, 24471, 32628, 48942, 97884.
What is 97884 in binary?
10111111001011100 (hexadecimal 17E5C, octal 277134).
What is the square root of 97884?
About 312.8642, exactly 6√2719.
Is 97884 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 97884?
97884 is a Harshad number: divisible by its digit sum 36.