The number 97968
97968 is a composite number with 40 divisors. Its prime factorisation is × 3 × 13 × 157. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104 … 97968.
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How to work it out
- 1
What is special about 97968: a Harshad number: divisible by its digit sum 39.
- 2
97968 is composite. Its prime factorisation is
- 3
The divisors add up to 274288; without 97968 itself that is 176320, so 97968 is abundant (176320 is more than 97968). Euler's totient φ(97968) = 29952 numbers up to 97968 share no factor with it.
- 4
The digits of 97968 add up to 39, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 190 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97968 = 2^{4} \times 3 \times 13 \times 157 \]97968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 274288 |
| Euler totient φ(n) | 29952 |
| Square | 9597729024 |
| Cube | 940270317023232 |
| Square root | 312.998403 (= 4√6123) |
| Digit sum / digital root | 39 / 3 |
| Collatz steps to 1 | 190 |
| Scientific notation | 9.7968 × |
97968 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand nine hundred and sixty-eight |
| Binary (base 2) | 10111111010110000 |
| Octal (base 8) | 277260 |
| Hexadecimal (base 16) | 17EB0 |
| Base 3 | 11222101110 |
| As time | 97968 seconds = 27 h 12 min 48 s |
Is 97968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97968 ÷ 2 = 48984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97968 ÷ 3 = 32656) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97968 ÷ 4 = 24492) | 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 (97968 ÷ 6 = 16328) | 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 (97968 ÷ 8 = 12246) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (97968 ÷ 12 = 8164) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97968 a prime number?
No. 97968 = × 3 × 13 × 157, so it is divisible by 2.
What are the factors of 97968?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 157, 208, 312, 314, 471, 624, 628, 942, 1256, 1884, 2041, 2512, 3768, 4082, 6123, 7536, 8164, 12246, 16328, 24492, 32656, 48984, 97968.
What is 97968 in binary?
10111111010110000 (hexadecimal 17EB0, octal 277260).
What is the square root of 97968?
About 312.9984, exactly 4√6123.
Is 97968 divisible by 3?
Yes. Its digits add up to 39, a multiple of 3.
What is special about the number 97968?
97968 is a Harshad number: divisible by its digit sum 39.