The number 72416
72416 is a composite number with 24 divisors. Its prime factorisation is × 31 × 73. Divisors (24): 1, 2, 4, 8, 16, 31, 32, 62, 73, 124, 146, 248, 292, 496, 584, 992 … 72416.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
72416 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72416 is composite. Its prime factorisation is
- 3
The divisors add up to 149184; without 72416 itself that is 76768, so 72416 is abundant (76768 is more than 72416). Euler's totient φ(72416) = 34560 numbers up to 72416 share no factor with it.
- 4
The digits of 72416 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72416 = 2^{5} \times 31 \times 73 \]72416 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 149184 |
| Euler totient φ(n) | 34560 |
| Square | 5244077056 |
| Cube | 379755084087296 |
| Square root | 269.102211 (= 4√4526) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 42 |
| Scientific notation | 7.2416 × |
72416 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand four hundred and sixteen |
| Binary (base 2) | 10001101011100000 |
| Octal (base 8) | 215340 |
| Hexadecimal (base 16) | 11AE0 |
| Base 3 | 10200100002 |
| As time | 72416 seconds = 20 h 6 min 56 s |
Is 72416 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72416 ÷ 2 = 36208) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72416 ÷ 4 = 18104) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (72416 ÷ 8 = 9052) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72416 a prime number?
No. 72416 = × 31 × 73, so it is divisible by 2.
What are the factors of 72416?
1, 2, 4, 8, 16, 31, 32, 62, 73, 124, 146, 248, 292, 496, 584, 992, 1168, 2263, 2336, 4526, 9052, 18104, 36208, 72416.
What is 72416 in binary?
10001101011100000 (hexadecimal 11AE0, octal 215340).
What is the square root of 72416?
About 269.1022, exactly 4√4526.
Is 72416 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 72416?
It is a composite number with 24 divisors.