The number 22197
22197 is a binary palindrome (101011010110101). Its prime factorisation is 3 × × 151. Divisors (12): 1, 3, 7, 21, 49, 147, 151, 453, 1057, 3171, 7399, 22197.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 22197: a binary palindrome (101011010110101); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
22197 is composite. Its prime factorisation is
- 3
The divisors add up to 34656; without 22197 itself that is 12459, so 22197 is deficient (12459 is less than 22197). Euler's totient φ(22197) = 12600 numbers up to 22197 share no factor with it.
- 4
The digits of 22197 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 69 steps to reach 1.
LaTeX source of the formulas on this page
\[ 22197 = 3 \times 7^{2} \times 151 \]22197 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 34656 |
| Euler totient φ(n) | 12600 |
| Square | 492706809 |
| Cube | 10936613039373 |
| Square root | 148.986577 (= 7√453) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 69 |
| Scientific notation | 2.2197 × |
22197 in other forms
| Form | Value |
|---|---|
| In words | twenty-two thousand one hundred and ninety-seven |
| Binary (base 2) | 101011010110101 |
| Octal (base 8) | 53265 |
| Hexadecimal (base 16) | 56B5 |
| Base 3 | 1010110010 |
| As time | 22197 seconds = 6 h 9 min 57 s |
Is 22197 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 (22197 ÷ 3 = 7399) | 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 2) | 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 (22197 ÷ 7 = 3171) | 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 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 22197 a prime number?
No. 22197 = 3 × × 151, so it is divisible by 3.
What are the factors of 22197?
1, 3, 7, 21, 49, 147, 151, 453, 1057, 3171, 7399, 22197.
What is 22197 in binary?
101011010110101 (hexadecimal 56B5, octal 53265).
What is the square root of 22197?
About 148.9866, exactly 7√453.
Is 22197 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 22197?
22197 is a binary palindrome (101011010110101); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.