The number 1900
1900 is a composite number with 18 divisors. Its prime factorisation is × × 19. Divisors (18): 1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 380, 475 … 1900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1900: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
1900 is composite. Its prime factorisation is
- 3
The divisors add up to 4340; without 1900 itself that is 2440, so 1900 is abundant (2440 is more than 1900). Euler's totient φ(1900) = 720 numbers up to 1900 share no factor with it.
- 4
The digits of 1900 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1900 = 2^{2} \times 5^{2} \times 19 \]1900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 4340 |
| Euler totient φ(n) | 720 |
| Square | 3610000 |
| Cube | 6859000000 |
| Square root | 43.588989 (= 10√19) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.9 × |
1900 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred |
| Roman numerals | MCM |
| Binary (base 2) | 11101101100 |
| Octal (base 8) | 3554 |
| Hexadecimal (base 16) | 76C |
| Base 3 | 2121101 |
| As time | 1900 seconds = 31 min 40 s |
Is 1900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1900 ÷ 2 = 950) | 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 (1900 ÷ 4 = 475) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1900 ÷ 5 = 380) | 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 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1900 ÷ 10 = 190) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | 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 1900 a prime number?
No. 1900 = × × 19, so it is divisible by 2.
What are the factors of 1900?
1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 380, 475, 950, 1900.
What is 1900 in binary?
11101101100 (hexadecimal 76C, octal 3554).
What is the square root of 1900?
About 43.5890, exactly 10√19.
What is 1900 in Roman numerals?
MCM.
Is 1900 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 1900?
1900 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.