The number 97664
97664 is a composite number with 32 divisors. Its prime factorisation is × 7 × 109. Divisors (32): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 109, 112, 128, 218, 224 … 97664.
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How to work it out
- 1
What is special about 97664: a Harshad number: divisible by its digit sum 32.
- 2
97664 is composite. Its prime factorisation is
- 3
The divisors add up to 224400; without 97664 itself that is 126736, so 97664 is abundant (126736 is more than 97664). Euler's totient φ(97664) = 41472 numbers up to 97664 share no factor with it.
- 4
The digits of 97664 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 159 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97664 = 2^{7} \times 7 \times 109 \]97664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 224400 |
| Euler totient φ(n) | 41472 |
| Square | 9538256896 |
| Cube | 931544321490944 |
| Square root | 312.512400 (= 8√1526) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 159 |
| Scientific notation | 9.7664 × |
97664 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand six hundred and sixty-four |
| Binary (base 2) | 10111110110000000 |
| Octal (base 8) | 276600 |
| Hexadecimal (base 16) | 17D80 |
| Base 3 | 11221222012 |
| As time | 97664 seconds = 27 h 7 min 44 s |
Is 97664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97664 ÷ 2 = 48832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97664 ÷ 4 = 24416) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (97664 ÷ 7 = 13952) | 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 (97664 ÷ 8 = 12208) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97664 a prime number?
No. 97664 = × 7 × 109, so it is divisible by 2.
What are the factors of 97664?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 109, 112, 128, 218, 224, 436, 448, 763, 872, 896, 1526, 1744, 3052, 3488, 6104, 6976, 12208, 13952, 24416, 48832, 97664.
What is 97664 in binary?
10111110110000000 (hexadecimal 17D80, octal 276600).
What is the square root of 97664?
About 312.5124, exactly 8√1526.
Is 97664 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 97664?
97664 is a Harshad number: divisible by its digit sum 32.