The number 97200
97200 is a composite number with 90 divisors. Its prime factorisation is × × . Divisors (90): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 97200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 97200: a Harshad number: divisible by its digit sum 18.
- 2
97200 is composite. Its prime factorisation is
- 3
The divisors add up to 349804; without 97200 itself that is 252604, so 97200 is abundant (252604 is more than 97200). Euler's totient φ(97200) = 25920 numbers up to 97200 share no factor with it.
- 4
The digits of 97200 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 66 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97200 = 2^{4} \times 3^{5} \times 5^{2} \]97200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 90 |
| Sum of divisors | 349804 |
| Euler totient φ(n) | 25920 |
| Square | 9447840000 |
| Cube | 918330048000000 |
| Square root | 311.769145 (= 180√3) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 66 |
| Scientific notation | 9.72 × |
97200 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand two hundred |
| Binary (base 2) | 10111101110110000 |
| Octal (base 8) | 275660 |
| Hexadecimal (base 16) | 17BB0 |
| Base 3 | 11221100000 |
| As time | 97200 seconds = 27 h 0 min 0 s |
Is 97200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97200 ÷ 2 = 48600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (97200 ÷ 3 = 32400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (97200 ÷ 4 = 24300) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (97200 ÷ 5 = 19440) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (97200 ÷ 6 = 16200) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (97200 ÷ 8 = 12150) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (97200 ÷ 9 = 10800) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (97200 ÷ 10 = 9720) | 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 | Yes (97200 ÷ 12 = 8100) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97200 a prime number?
No. 97200 = × × , so it is divisible by 2.
What are the factors of 97200?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 243, 270, 300, 324, 360, 400, 405, 432, 450, 486, 540, 600, 648, 675, 720, 810, 900, 972, 1080, 1200, 1215, 1296, 1350, 1620, 1800, 1944, 2025, 2160, 2430, 2700, 3240, 3600, 3888, 4050, 4860, 5400, 6075, 6480, 8100, 9720, 10800, 12150, 16200, 19440, 24300, 32400, 48600, 97200.
What is 97200 in binary?
10111101110110000 (hexadecimal 17BB0, octal 275660).
What is the square root of 97200?
About 311.7691, exactly 180√3.
Is 97200 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 97200?
97200 is a Harshad number: divisible by its digit sum 18.