The number 80400
80400 is a composite number with 60 divisors. Its prime factorisation is × 3 × × 67. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40 … 80400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 80400: a Harshad number: divisible by its digit sum 12.
- 2
80400 is composite. Its prime factorisation is
- 3
The divisors add up to 261392; without 80400 itself that is 180992, so 80400 is abundant (180992 is more than 80400). Euler's totient φ(80400) = 21120 numbers up to 80400 share no factor with it.
- 4
The digits of 80400 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 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 80400 = 2^{4} \times 3 \times 5^{2} \times 67 \]80400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 261392 |
| Euler totient φ(n) | 21120 |
| Square | 6464160000 |
| Cube | 519718464000000 |
| Square root | 283.548938 (= 20√201) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 120 |
| Scientific notation | 8.04 × |
80400 in other forms
| Form | Value |
|---|---|
| In words | eighty thousand four hundred |
| Binary (base 2) | 10011101000010000 |
| Octal (base 8) | 235020 |
| Hexadecimal (base 16) | 13A10 |
| Base 3 | 11002021210 |
| As time | 80400 seconds = 22 h 20 min 0 s |
Is 80400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (80400 ÷ 2 = 40200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (80400 ÷ 3 = 26800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (80400 ÷ 4 = 20100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (80400 ÷ 5 = 16080) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (80400 ÷ 6 = 13400) | 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 (80400 ÷ 8 = 10050) | 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 (80400 ÷ 10 = 8040) | 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 (80400 ÷ 12 = 6700) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 80400 a prime number?
No. 80400 = × 3 × × 67, so it is divisible by 2.
What are the factors of 80400?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 67, 75, 80, 100, 120, 134, 150, 200, 201, 240, 268, 300, 335, 400, 402, 536, 600, 670, 804, 1005, 1072, 1200, 1340, 1608, 1675, 2010, 2680, 3216, 3350, 4020, 5025, 5360, 6700, 8040, 10050, 13400, 16080, 20100, 26800, 40200, 80400.
What is 80400 in binary?
10011101000010000 (hexadecimal 13A10, octal 235020).
What is the square root of 80400?
About 283.5489, exactly 20√201.
Is 80400 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 80400?
80400 is a Harshad number: divisible by its digit sum 12.