The number 72198
72198 is a composite number with 32 divisors. Its prime factorisation is 2 × × 7 × 191. Divisors (32): 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 191 … 72198.
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How to work it out
- 1
What is special about 72198: a Harshad number: divisible by its digit sum 27.
- 2
72198 is composite. Its prime factorisation is
- 3
The divisors add up to 184320; without 72198 itself that is 112122, so 72198 is abundant (112122 is more than 72198). Euler's totient φ(72198) = 20520 numbers up to 72198 share no factor with it.
- 4
The digits of 72198 add up to 27, 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
\[ 72198 = 2 \times 3^{3} \times 7 \times 191 \]72198 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 184320 |
| Euler totient φ(n) | 20520 |
| Square | 5212551204 |
| Cube | 376335771826392 |
| Square root | 268.696855 (= 3√8022) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 68 |
| Scientific notation | 7.2198 × |
72198 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred and ninety-eight |
| Binary (base 2) | 10001101000000110 |
| Octal (base 8) | 215006 |
| Hexadecimal (base 16) | 11A06 |
| Base 3 | 10200001000 |
| As time | 72198 seconds = 20 h 3 min 18 s |
Is 72198 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72198 ÷ 2 = 36099) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72198 ÷ 3 = 24066) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72198 ÷ 6 = 12033) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (72198 ÷ 7 = 10314) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72198 ÷ 9 = 8022) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72198 a prime number?
No. 72198 = 2 × × 7 × 191, so it is divisible by 2.
What are the factors of 72198?
1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 191, 378, 382, 573, 1146, 1337, 1719, 2674, 3438, 4011, 5157, 8022, 10314, 12033, 24066, 36099, 72198.
What is 72198 in binary?
10001101000000110 (hexadecimal 11A06, octal 215006).
What is the square root of 72198?
About 268.6969, exactly 3√8022.
Is 72198 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 72198?
72198 is a Harshad number: divisible by its digit sum 27.