The number 97836
97836 is a composite number with 24 divisors. Its prime factorisation is × 3 × 31 × 263. Divisors (24): 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 263, 372, 526, 789, 1052 … 97836.
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How to work it out
- 1
What is special about 97836: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
97836 is composite. Its prime factorisation is
- 3
The divisors add up to 236544; without 97836 itself that is 138708, so 97836 is abundant (138708 is more than 97836). Euler's totient φ(97836) = 31440 numbers up to 97836 share no factor with it.
- 4
The digits of 97836 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 159 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97836 = 2^{2} \times 3 \times 31 \times 263 \]97836 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 236544 |
| Euler totient φ(n) | 31440 |
| Square | 9571882896 |
| Cube | 936474735013056 |
| Square root | 312.787468 (= 2√24459) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 159 |
| Scientific notation | 9.7836 × |
97836 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand eight hundred and thirty-six |
| Binary (base 2) | 10111111000101100 |
| Octal (base 8) | 277054 |
| Hexadecimal (base 16) | 17E2C |
| Base 3 | 11222012120 |
| As time | 97836 seconds = 27 h 10 min 36 s |
Is 97836 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97836 ÷ 2 = 48918) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97836 ÷ 3 = 32612) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97836 ÷ 4 = 24459) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (97836 ÷ 6 = 16306) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 (97836 ÷ 12 = 8153) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97836 a prime number?
No. 97836 = × 3 × 31 × 263, so it is divisible by 2.
What are the factors of 97836?
1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 263, 372, 526, 789, 1052, 1578, 3156, 8153, 16306, 24459, 32612, 48918, 97836.
What is 97836 in binary?
10111111000101100 (hexadecimal 17E2C, octal 277054).
What is the square root of 97836?
About 312.7875, exactly 2√24459.
Is 97836 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 97836?
97836 is a happy number: repeatedly adding the squares of its digits reaches 1.