The number 7200
7200 is a composite number with 54 divisors. Its prime factorisation is × × . Divisors (54): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 7200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7200: a Harshad number: divisible by its digit sum 9.
- 2
7200 is composite. Its prime factorisation is
- 3
The divisors add up to 25389; without 7200 itself that is 18189, so 7200 is abundant (18189 is more than 7200). Euler's totient φ(7200) = 1920 numbers up to 7200 share no factor with it.
- 4
The digits of 7200 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 57 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7200 = 2^{5} \times 3^{2} \times 5^{2} \]7200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 25389 |
| Euler totient φ(n) | 1920 |
| Square | 51840000 |
| Cube | 373248000000 |
| Square root | 84.852814 (= 60√2) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 57 |
| Scientific notation | 7.2 × |
7200 in other forms
| Form | Value |
|---|---|
| In words | seven thousand two hundred |
| Binary (base 2) | 1110000100000 |
| Octal (base 8) | 16040 |
| Hexadecimal (base 16) | 1C20 |
| Base 3 | 100212200 |
| As time | 7200 seconds = 2 h 0 min 0 s |
Is 7200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7200 ÷ 2 = 3600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7200 ÷ 3 = 2400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7200 ÷ 4 = 1800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7200 ÷ 5 = 1440) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7200 ÷ 6 = 1200) | 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 | Yes (7200 ÷ 8 = 900) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (7200 ÷ 9 = 800) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (7200 ÷ 10 = 720) | 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 | Yes (7200 ÷ 12 = 600) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7200 a prime number?
No. 7200 = × × , so it is divisible by 2.
What are the factors of 7200?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 200, 225, 240, 288, 300, 360, 400, 450, 480, 600, 720, 800, 900, 1200, 1440, 1800, 2400, 3600, 7200.
What is 7200 in binary?
1110000100000 (hexadecimal 1C20, octal 16040).
What is the square root of 7200?
About 84.8528, exactly 60√2.
Is 7200 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 7200?
7200 is a Harshad number: divisible by its digit sum 9.