The number 19900
19900 is a triangular number: 1 + 2 + … + 199 = 19900. Its prime factorisation is × × 199. Divisors (18): 1, 2, 4, 5, 10, 20, 25, 50, 100, 199, 398, 796, 995, 1990, 3980, 4975 … 19900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 19900: a triangular number: 1 + 2 + … + 199 = 19900.
- 2
19900 is composite. Its prime factorisation is
- 3
The divisors add up to 43400; without 19900 itself that is 23500, so 19900 is abundant (23500 is more than 19900). Euler's totient φ(19900) = 7920 numbers up to 19900 share no factor with it.
- 4
The digits of 19900 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 74 steps to reach 1.
LaTeX source of the formulas on this page
\[ 19900 = 2^{2} \times 5^{2} \times 199 \]19900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 43400 |
| Euler totient φ(n) | 7920 |
| Square | 396010000 |
| Cube | 7880599000000 |
| Square root | 141.067360 (= 10√199) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 74 |
| Scientific notation | 1.99 × |
19900 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand nine hundred |
| Binary (base 2) | 100110110111100 |
| Octal (base 8) | 46674 |
| Hexadecimal (base 16) | 4DBC |
| Base 3 | 1000022001 |
| As time | 19900 seconds = 5 h 31 min 40 s |
Is 19900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (19900 ÷ 2 = 9950) | 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 (19900 ÷ 4 = 4975) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (19900 ÷ 5 = 3980) | 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 6) | 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 (19900 ÷ 10 = 1990) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 19900 a prime number?
No. 19900 = × × 199, so it is divisible by 2.
What are the factors of 19900?
1, 2, 4, 5, 10, 20, 25, 50, 100, 199, 398, 796, 995, 1990, 3980, 4975, 9950, 19900.
What is 19900 in binary?
100110110111100 (hexadecimal 4DBC, octal 46674).
What is the square root of 19900?
About 141.0674, exactly 10√199.
Is 19900 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 19900?
19900 is a triangular number: 1 + 2 + … + 199 = 19900.