The number 1998
1998 is a composite number with 16 divisors. Its prime factorisation is 2 × × 37. Divisors (16): 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1998: a Harshad number: divisible by its digit sum 27.
- 2
1998 is composite. Its prime factorisation is
- 3
The divisors add up to 4560; without 1998 itself that is 2562, so 1998 is abundant (2562 is more than 1998). Euler's totient φ(1998) = 648 numbers up to 1998 share no factor with it.
- 4
The digits of 1998 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1998 = 2 \times 3^{3} \times 37 \]1998 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 4560 |
| Euler totient φ(n) | 648 |
| Square | 3992004 |
| Cube | 7976023992 |
| Square root | 44.698993 (= 3√222) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.998 × |
1998 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and ninety-eight |
| Roman numerals | MCMXCVIII |
| Binary (base 2) | 11111001110 |
| Octal (base 8) | 3716 |
| Hexadecimal (base 16) | 7CE |
| Base 3 | 2202000 |
| As time | 1998 seconds = 33 min 18 s |
Is 1998 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1998 ÷ 2 = 999) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1998 ÷ 3 = 666) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1998 ÷ 6 = 333) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1998 ÷ 9 = 222) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1998 a prime number?
No. 1998 = 2 × × 37, so it is divisible by 2.
What are the factors of 1998?
1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998.
What is 1998 in binary?
11111001110 (hexadecimal 7CE, octal 3716).
What is the square root of 1998?
About 44.6990, exactly 3√222.
What is 1998 in Roman numerals?
MCMXCVIII.
Is 1998 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 1998?
1998 is a Harshad number: divisible by its digit sum 27.