The number 20400
20400 is a composite number with 60 divisors. Its prime factorisation is × 3 × × 17. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30 … 20400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20400: a Harshad number: divisible by its digit sum 6.
- 2
20400 is composite. Its prime factorisation is
- 3
The divisors add up to 69192; without 20400 itself that is 48792, so 20400 is abundant (48792 is more than 20400). Euler's totient φ(20400) = 5120 numbers up to 20400 share no factor with it.
- 4
The digits of 20400 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 87 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20400 = 2^{4} \times 3 \times 5^{2} \times 17 \]20400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 69192 |
| Euler totient φ(n) | 5120 |
| Square | 416160000 |
| Cube | 8489664000000 |
| Square root | 142.828569 (= 20√51) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 87 |
| Scientific notation | 2.04 × |
20400 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand four hundred |
| Binary (base 2) | 100111110110000 |
| Octal (base 8) | 47660 |
| Hexadecimal (base 16) | 4FB0 |
| Base 3 | 1000222120 |
| As time | 20400 seconds = 5 h 40 min 0 s |
Is 20400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20400 ÷ 2 = 10200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (20400 ÷ 3 = 6800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20400 ÷ 4 = 5100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (20400 ÷ 5 = 4080) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (20400 ÷ 6 = 3400) | 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 (20400 ÷ 8 = 2550) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (20400 ÷ 10 = 2040) | 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 (20400 ÷ 12 = 1700) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20400 a prime number?
No. 20400 = × 3 × × 17, so it is divisible by 2.
What are the factors of 20400?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 34, 40, 48, 50, 51, 60, 68, 75, 80, 85, 100, 102, 120, 136, 150, 170, 200, 204, 240, 255, 272, 300, 340, 400, 408, 425, 510, 600, 680, 816, 850, 1020, 1200, 1275, 1360, 1700, 2040, 2550, 3400, 4080, 5100, 6800, 10200, 20400.
What is 20400 in binary?
100111110110000 (hexadecimal 4FB0, octal 47660).
What is the square root of 20400?
About 142.8286, exactly 20√51.
Is 20400 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 20400?
20400 is a Harshad number: divisible by its digit sum 6.