The number 67221
67221 is a composite number with 24 divisors. Its prime factorisation is × 7 × 11 × 97. Divisors (24): 1, 3, 7, 9, 11, 21, 33, 63, 77, 97, 99, 231, 291, 679, 693, 873 … 67221.
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How to work it out
- 1
What is special about 67221: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
67221 is composite. Its prime factorisation is
- 3
The divisors add up to 122304; without 67221 itself that is 55083, so 67221 is deficient (55083 is less than 67221). Euler's totient φ(67221) = 34560 numbers up to 67221 share no factor with it.
- 4
The digits of 67221 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 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67221 = 3^{2} \times 7 \times 11 \times 97 \]67221 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 122304 |
| Euler totient φ(n) | 34560 |
| Square | 4518662841 |
| Cube | 303749034834861 |
| Square root | 259.270129 (= 3√7469) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 68 |
| Scientific notation | 6.7221 × |
67221 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand two hundred and twenty-one |
| Binary (base 2) | 10000011010010101 |
| Octal (base 8) | 203225 |
| Hexadecimal (base 16) | 10695 |
| Base 3 | 10102012200 |
| As time | 67221 seconds = 18 h 40 min 21 s |
Is 67221 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67221 ÷ 3 = 22407) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (67221 ÷ 7 = 9603) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (67221 ÷ 9 = 7469) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (67221 ÷ 11 = 6111) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67221 a prime number?
No. 67221 = × 7 × 11 × 97, so it is divisible by 3.
What are the factors of 67221?
1, 3, 7, 9, 11, 21, 33, 63, 77, 97, 99, 231, 291, 679, 693, 873, 1067, 2037, 3201, 6111, 7469, 9603, 22407, 67221.
What is 67221 in binary?
10000011010010101 (hexadecimal 10695, octal 203225).
What is the square root of 67221?
About 259.2701, exactly 3√7469.
Is 67221 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 67221?
67221 is a happy number: repeatedly adding the squares of its digits reaches 1.