The number 19920
19920 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 83. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 19920.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 19920: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
19920 is composite. Its prime factorisation is
- 3
The divisors add up to 62496; without 19920 itself that is 42576, so 19920 is abundant (42576 is more than 19920). Euler's totient φ(19920) = 5248 numbers up to 19920 share no factor with it.
- 4
The digits of 19920 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 92 steps to reach 1.
LaTeX source of the formulas on this page
\[ 19920 = 2^{4} \times 3 \times 5 \times 83 \]19920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 62496 |
| Euler totient φ(n) | 5248 |
| Square | 396806400 |
| Cube | 7904383488000 |
| Square root | 141.138230 (= 4√1245) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 92 |
| Scientific notation | 1.992 × |
19920 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand nine hundred and twenty |
| Binary (base 2) | 100110111010000 |
| Octal (base 8) | 46720 |
| Hexadecimal (base 16) | 4DD0 |
| Base 3 | 1000022210 |
| As time | 19920 seconds = 5 h 32 min 0 s |
Is 19920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (19920 ÷ 2 = 9960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (19920 ÷ 3 = 6640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (19920 ÷ 4 = 4980) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (19920 ÷ 5 = 3984) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (19920 ÷ 6 = 3320) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (19920 ÷ 8 = 2490) | 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 (19920 ÷ 10 = 1992) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (19920 ÷ 12 = 1660) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 19920 a prime number?
No. 19920 = × 3 × 5 × 83, so it is divisible by 2.
What are the factors of 19920?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 83, 120, 166, 240, 249, 332, 415, 498, 664, 830, 996, 1245, 1328, 1660, 1992, 2490, 3320, 3984, 4980, 6640, 9960, 19920.
What is 19920 in binary?
100110111010000 (hexadecimal 4DD0, octal 46720).
What is the square root of 19920?
About 141.1382, exactly 4√1245.
Is 19920 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 19920?
19920 is a happy number: repeatedly adding the squares of its digits reaches 1.