The number 1920
1920 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 1920.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1920: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
1920 is composite. Its prime factorisation is
- 3
The divisors add up to 6120; without 1920 itself that is 4200, so 1920 is abundant (4200 is more than 1920). Euler's totient φ(1920) = 512 numbers up to 1920 share no factor with it.
- 4
The digits of 1920 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1920 = 2^{7} \times 3 \times 5 \]1920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 6120 |
| Euler totient φ(n) | 512 |
| Square | 3686400 |
| Cube | 7077888000 |
| Square root | 43.817805 (= 8√30) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 24 |
| Scientific notation | 1.92 × |
1920 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and twenty |
| Roman numerals | MCMXX |
| Binary (base 2) | 11110000000 |
| Octal (base 8) | 3600 |
| Hexadecimal (base 16) | 780 |
| Base 3 | 2122010 |
| As time | 1920 seconds = 32 min 0 s |
Is 1920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1920 ÷ 2 = 960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1920 ÷ 3 = 640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1920 ÷ 4 = 480) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1920 ÷ 5 = 384) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1920 ÷ 6 = 320) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (1920 ÷ 8 = 240) | 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 | Yes (1920 ÷ 10 = 192) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1920 ÷ 12 = 160) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1920 a prime number?
No. 1920 = × 3 × 5, so it is divisible by 2.
What are the factors of 1920?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1920.
What is 1920 in binary?
11110000000 (hexadecimal 780, octal 3600).
What is the square root of 1920?
About 43.8178, exactly 8√30.
What is 1920 in Roman numerals?
MCMXX.
Is 1920 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1920?
1920 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.