The number 72116
72116 is a composite number with 18 divisors. Its prime factorisation is × × 149. Divisors (18): 1, 2, 4, 11, 22, 44, 121, 149, 242, 298, 484, 596, 1639, 3278, 6556, 18029 … 72116.
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How to work it out
- 1
What is special about 72116: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
72116 is composite. Its prime factorisation is
- 3
The divisors add up to 139650; without 72116 itself that is 67534, so 72116 is deficient (67534 is less than 72116). Euler's totient φ(72116) = 32560 numbers up to 72116 share no factor with it.
- 4
The digits of 72116 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72116 = 2^{2} \times 11^{2} \times 149 \]72116 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 139650 |
| Euler totient φ(n) | 32560 |
| Square | 5200717456 |
| Cube | 375054940056896 |
| Square root | 268.544224 (= 22√149) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 94 |
| Scientific notation | 7.2116 × |
72116 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred and sixteen |
| Binary (base 2) | 10001100110110100 |
| Octal (base 8) | 214664 |
| Hexadecimal (base 16) | 119B4 |
| Base 3 | 10122220222 |
| As time | 72116 seconds = 20 h 1 min 56 s |
Is 72116 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72116 ÷ 2 = 36058) | 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 (72116 ÷ 4 = 18029) | 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 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 | Yes (72116 ÷ 11 = 6556) | 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 72116 a prime number?
No. 72116 = × × 149, so it is divisible by 2.
What are the factors of 72116?
1, 2, 4, 11, 22, 44, 121, 149, 242, 298, 484, 596, 1639, 3278, 6556, 18029, 36058, 72116.
What is 72116 in binary?
10001100110110100 (hexadecimal 119B4, octal 214664).
What is the square root of 72116?
About 268.5442, exactly 22√149.
Is 72116 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 72116?
72116 is a happy number: repeatedly adding the squares of its digits reaches 1.