The number 19840
19840 is a composite number with 32 divisors. Its prime factorisation is × 5 × 31. Divisors (32): 1, 2, 4, 5, 8, 10, 16, 20, 31, 32, 40, 62, 64, 80, 124, 128 … 19840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
19840 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
19840 is composite. Its prime factorisation is
- 3
The divisors add up to 48960; without 19840 itself that is 29120, so 19840 is abundant (29120 is more than 19840). Euler's totient φ(19840) = 7680 numbers up to 19840 share no factor with it.
- 4
The digits of 19840 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 92 steps to reach 1.
LaTeX source of the formulas on this page
\[ 19840 = 2^{7} \times 5 \times 31 \]19840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 48960 |
| Euler totient φ(n) | 7680 |
| Square | 393625600 |
| Cube | 7809531904000 |
| Square root | 140.854535 (= 8√310) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 92 |
| Scientific notation | 1.984 × |
19840 in other forms
| Form | Value |
|---|---|
| In words | nineteen thousand eight hundred and forty |
| Binary (base 2) | 100110110000000 |
| Octal (base 8) | 46600 |
| Hexadecimal (base 16) | 4D80 |
| Base 3 | 1000012211 |
| As time | 19840 seconds = 5 h 30 min 40 s |
Is 19840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (19840 ÷ 2 = 9920) | 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 (19840 ÷ 4 = 4960) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (19840 ÷ 5 = 3968) | 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 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 (19840 ÷ 8 = 2480) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (19840 ÷ 10 = 1984) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 19840 a prime number?
No. 19840 = × 5 × 31, so it is divisible by 2.
What are the factors of 19840?
1, 2, 4, 5, 8, 10, 16, 20, 31, 32, 40, 62, 64, 80, 124, 128, 155, 160, 248, 310, 320, 496, 620, 640, 992, 1240, 1984, 2480, 3968, 4960, 9920, 19840.
What is 19840 in binary?
100110110000000 (hexadecimal 4D80, octal 46600).
What is the square root of 19840?
About 140.8545, exactly 8√310.
Is 19840 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 19840?
It is a composite number with 32 divisors.