The number 97002
97002 is a composite number with 24 divisors. Its prime factorisation is 2 × × 17 × 317. Divisors (24): 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306, 317, 634, 951, 1902 … 97002.
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How to work it out
- 1
What is special about 97002: a Harshad number: divisible by its digit sum 18.
- 2
97002 is composite. Its prime factorisation is
- 3
The divisors add up to 223236; without 97002 itself that is 126234, so 97002 is abundant (126234 is more than 97002). Euler's totient φ(97002) = 30336 numbers up to 97002 share no factor with it.
- 4
The digits of 97002 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 146 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97002 = 2 \times 3^{2} \times 17 \times 317 \]97002 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 223236 |
| Euler totient φ(n) | 30336 |
| Square | 9409388004 |
| Cube | 912729455164008 |
| Square root | 311.451441 (= 3√10778) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 146 |
| Scientific notation | 9.7002 × |
97002 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand and two |
| Binary (base 2) | 10111101011101010 |
| Octal (base 8) | 275352 |
| Hexadecimal (base 16) | 17AEA |
| Base 3 | 11221001200 |
| As time | 97002 seconds = 26 h 56 min 42 s |
Is 97002 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97002 ÷ 2 = 48501) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97002 ÷ 3 = 32334) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 (97002 ÷ 6 = 16167) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (97002 ÷ 9 = 10778) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97002 a prime number?
No. 97002 = 2 × × 17 × 317, so it is divisible by 2.
What are the factors of 97002?
1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306, 317, 634, 951, 1902, 2853, 5389, 5706, 10778, 16167, 32334, 48501, 97002.
What is 97002 in binary?
10111101011101010 (hexadecimal 17AEA, octal 275352).
What is the square root of 97002?
About 311.4514, exactly 3√10778.
Is 97002 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 97002?
97002 is a Harshad number: divisible by its digit sum 18.