The number 1992
1992 is a composite number with 16 divisors. Its prime factorisation is × 3 × 83. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 83, 166, 249, 332, 498, 664, 996, 1992.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1992: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1992 is composite. Its prime factorisation is
- 3
The divisors add up to 5040; without 1992 itself that is 3048, so 1992 is abundant (3048 is more than 1992). Euler's totient φ(1992) = 656 numbers up to 1992 share no factor with it.
- 4
The digits of 1992 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1992 = 2^{3} \times 3 \times 83 \]1992 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 5040 |
| Euler totient φ(n) | 656 |
| Square | 3968064 |
| Cube | 7904383488 |
| Square root | 44.631827 (= 2√498) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.992 × |
1992 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and ninety-two |
| Roman numerals | MCMXCII |
| Binary (base 2) | 11111001000 |
| Octal (base 8) | 3710 |
| Hexadecimal (base 16) | 7C8 |
| Base 3 | 2201210 |
| As time | 1992 seconds = 33 min 12 s |
Is 1992 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1992 ÷ 2 = 996) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1992 ÷ 3 = 664) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1992 ÷ 4 = 498) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1992 ÷ 6 = 332) | 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 (1992 ÷ 8 = 249) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 | Yes (1992 ÷ 12 = 166) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1992 a prime number?
No. 1992 = × 3 × 83, so it is divisible by 2.
What are the factors of 1992?
1, 2, 3, 4, 6, 8, 12, 24, 83, 166, 249, 332, 498, 664, 996, 1992.
What is 1992 in binary?
11111001000 (hexadecimal 7C8, octal 3710).
What is the square root of 1992?
About 44.6318, exactly 2√498.
What is 1992 in Roman numerals?
MCMXCII.
Is 1992 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 1992?
1992 is a happy number: repeatedly adding the squares of its digits reaches 1.