The number 1600
1600 is a perfect square (40²). Its prime factorisation is × . Divisors (21): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160 … 1600.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1600: a perfect square (40²).
- 2
1600 is composite. Its prime factorisation is
- 3
The divisors add up to 3937; without 1600 itself that is 2337, so 1600 is abundant (2337 is more than 1600). Euler's totient φ(1600) = 640 numbers up to 1600 share no factor with it.
- 4
The digits of 1600 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1600 = 2^{6} \times 5^{2} \]1600 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 21 |
| Sum of divisors | 3937 |
| Euler totient φ(n) | 640 |
| Square | 2560000 |
| Cube | 4096000000 |
| Square root | 40 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.6 × |
| Perfect power |
1600 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred |
| Roman numerals | MDC |
| Binary (base 2) | 11001000000 |
| Octal (base 8) | 3100 |
| Hexadecimal (base 16) | 640 |
| Base 3 | 2012021 |
| As time | 1600 seconds = 26 min 40 s |
Is 1600 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1600 ÷ 2 = 800) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1600 ÷ 4 = 400) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1600 ÷ 5 = 320) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 (1600 ÷ 8 = 200) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1600 ÷ 10 = 160) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1600 a prime number?
No. 1600 = × , so it is divisible by 2.
What are the factors of 1600?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600.
What is 1600 in binary?
11001000000 (hexadecimal 640, octal 3100).
What is the square root of 1600?
40, because 40 × 40 = 1600.
What is 1600 in Roman numerals?
MDC.
Is 1600 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 1600?
1600 is a perfect square (40²).