The number 3600
3600 is a perfect square (60²). Its prime factorisation is × × . Divisors (45): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 3600.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3600: a perfect square (60²); a Harshad number: divisible by its digit sum 9.
- 2
3600 is composite. Its prime factorisation is
- 3
The divisors add up to 12493; without 3600 itself that is 8893, so 3600 is abundant (8893 is more than 3600). Euler's totient φ(3600) = 960 numbers up to 3600 share no factor with it.
- 4
The digits of 3600 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 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3600 = 2^{4} \times 3^{2} \times 5^{2} \]3600 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 45 |
| Sum of divisors | 12493 |
| Euler totient φ(n) | 960 |
| Square | 12960000 |
| Cube | 46656000000 |
| Square root | 60 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 56 |
| Scientific notation | 3.6 × |
| Perfect power |
3600 in other forms
| Form | Value |
|---|---|
| In words | three thousand six hundred |
| Roman numerals | MMMDC |
| Binary (base 2) | 111000010000 |
| Octal (base 8) | 7020 |
| Hexadecimal (base 16) | E10 |
| Base 3 | 11221100 |
| As time | 3600 seconds = 1 h 0 min 0 s |
Is 3600 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3600 ÷ 2 = 1800) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3600 ÷ 3 = 1200) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3600 ÷ 4 = 900) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3600 ÷ 5 = 720) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3600 ÷ 6 = 600) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (3600 ÷ 8 = 450) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3600 ÷ 9 = 400) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3600 ÷ 10 = 360) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3600 ÷ 12 = 300) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3600 a prime number?
No. 3600 = × × , so it is divisible by 2.
What are the factors of 3600?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600.
What is 3600 in binary?
111000010000 (hexadecimal E10, octal 7020).
What is the square root of 3600?
60, because 60 × 60 = 3600.
What is 3600 in Roman numerals?
MMMDC.
Is 3600 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 3600?
3600 is a perfect square (60²); a Harshad number: divisible by its digit sum 9.