The number 72400
72400 is a composite number with 30 divisors. Its prime factorisation is × × 181. Divisors (30): 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 181, 200, 362 … 72400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
72400 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72400 is composite. Its prime factorisation is
- 3
The divisors add up to 174902; without 72400 itself that is 102502, so 72400 is abundant (102502 is more than 72400). Euler's totient φ(72400) = 28800 numbers up to 72400 share no factor with it.
- 4
The digits of 72400 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72400 = 2^{4} \times 5^{2} \times 181 \]72400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 174902 |
| Euler totient φ(n) | 28800 |
| Square | 5241760000 |
| Cube | 379503424000000 |
| Square root | 269.072481 (= 20√181) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 42 |
| Scientific notation | 7.24 × |
72400 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand four hundred |
| Binary (base 2) | 10001101011010000 |
| Octal (base 8) | 215320 |
| Hexadecimal (base 16) | 11AD0 |
| Base 3 | 10200022111 |
| As time | 72400 seconds = 20 h 6 min 40 s |
Is 72400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72400 ÷ 2 = 36200) | 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 (72400 ÷ 4 = 18100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72400 ÷ 5 = 14480) | 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 6) | 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 (72400 ÷ 8 = 9050) | 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 (72400 ÷ 10 = 7240) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 72400 a prime number?
No. 72400 = × × 181, so it is divisible by 2.
What are the factors of 72400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 181, 200, 362, 400, 724, 905, 1448, 1810, 2896, 3620, 4525, 7240, 9050, 14480, 18100, 36200, 72400.
What is 72400 in binary?
10001101011010000 (hexadecimal 11AD0, octal 215320).
What is the square root of 72400?
About 269.0725, exactly 20√181.
Is 72400 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 72400?
It is a composite number with 30 divisors.