The number 72216
72216 is a composite number with 48 divisors. Its prime factorisation is × × 17 × 59. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 59, 68 … 72216.
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How to work it out
- 1
What is special about 72216: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
72216 is composite. Its prime factorisation is
- 3
The divisors add up to 210600; without 72216 itself that is 138384, so 72216 is abundant (138384 is more than 72216). Euler's totient φ(72216) = 22272 numbers up to 72216 share no factor with it.
- 4
The digits of 72216 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 187 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72216 = 2^{3} \times 3^{2} \times 17 \times 59 \]72216 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 210600 |
| Euler totient φ(n) | 22272 |
| Square | 5215150656 |
| Cube | 376617319773696 |
| Square root | 268.730348 (= 6√2006) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 187 |
| Scientific notation | 7.2216 × |
72216 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand two hundred and sixteen |
| Binary (base 2) | 10001101000011000 |
| Octal (base 8) | 215030 |
| Hexadecimal (base 16) | 11A18 |
| Base 3 | 10200001200 |
| As time | 72216 seconds = 20 h 3 min 36 s |
Is 72216 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72216 ÷ 2 = 36108) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72216 ÷ 3 = 24072) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72216 ÷ 4 = 18054) | 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 | Yes (72216 ÷ 6 = 12036) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (72216 ÷ 8 = 9027) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72216 ÷ 9 = 8024) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72216 ÷ 12 = 6018) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72216 a prime number?
No. 72216 = × × 17 × 59, so it is divisible by 2.
What are the factors of 72216?
1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 59, 68, 72, 102, 118, 136, 153, 177, 204, 236, 306, 354, 408, 472, 531, 612, 708, 1003, 1062, 1224, 1416, 2006, 2124, 3009, 4012, 4248, 6018, 8024, 9027, 12036, 18054, 24072, 36108, 72216.
What is 72216 in binary?
10001101000011000 (hexadecimal 11A18, octal 215030).
What is the square root of 72216?
About 268.7303, exactly 6√2006.
Is 72216 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72216?
72216 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.