The number 72105
72105 is a composite number with 32 divisors. Its prime factorisation is 3 × 5 × 11 × 19 × 23. Divisors (32): 1, 3, 5, 11, 15, 19, 23, 33, 55, 57, 69, 95, 115, 165, 209, 253 … 72105.
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How to work it out
- 1
What is special about 72105: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 15.
- 2
72105 is composite. Its prime factorisation is
- 3
The divisors add up to 138240; without 72105 itself that is 66135, so 72105 is deficient (66135 is less than 72105). Euler's totient φ(72105) = 31680 numbers up to 72105 share no factor with it.
- 4
The digits of 72105 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72105 = 3 \times 5 \times 11 \times 19 \times 23 \]
72105 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 138240 |
| Euler totient φ(n) | 31680 |
| Square | 5199131025 |
| Cube | 374883342557625 |
| Square root | 268.523742 |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 68 |
| Scientific notation | 7.2105 × |
72105 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred and five |
| Binary (base 2) | 10001100110101001 |
| Octal (base 8) | 214651 |
| Hexadecimal (base 16) | 119A9 |
| Base 3 | 10122220120 |
| As time | 72105 seconds = 20 h 1 min 45 s |
Is 72105 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 (72105 ÷ 3 = 24035) | 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 | Yes (72105 ÷ 5 = 14421) | 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 | No (remainder 5) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (72105 ÷ 11 = 6555) | 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 72105 a prime number?
No. 72105 = 3 × 5 × 11 × 19 × 23, so it is divisible by 3.
What are the factors of 72105?
1, 3, 5, 11, 15, 19, 23, 33, 55, 57, 69, 95, 115, 165, 209, 253, 285, 345, 437, 627, 759, 1045, 1265, 1311, 2185, 3135, 3795, 4807, 6555, 14421, 24035, 72105.
What is 72105 in binary?
10001100110101001 (hexadecimal 119A9, octal 214651).
What is the square root of 72105?
About 268.5237.
Is 72105 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 72105?
72105 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 15.