The number 72345
72345 is a composite number with 32 divisors. Its prime factorisation is 3 × 5 × 7 × 13 × 53. Divisors (32): 1, 3, 5, 7, 13, 15, 21, 35, 39, 53, 65, 91, 105, 159, 195, 265 … 72345.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72345: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
72345 is composite. Its prime factorisation is
- 3
The divisors add up to 145152; without 72345 itself that is 72807, so 72345 is abundant (72807 is more than 72345). Euler's totient φ(72345) = 29952 numbers up to 72345 share no factor with it.
- 4
The digits of 72345 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 81 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72345 = 3 \times 5 \times 7 \times 13 \times 53 \]
72345 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 145152 |
| Euler totient φ(n) | 29952 |
| Square | 5233799025 |
| Cube | 378639190463625 |
| Square root | 268.970259 |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 81 |
| Scientific notation | 7.2345 × |
72345 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand three hundred and forty-five |
| Binary (base 2) | 10001101010011001 |
| Octal (base 8) | 215231 |
| Hexadecimal (base 16) | 11A99 |
| Base 3 | 10200020110 |
| As time | 72345 seconds = 20 h 5 min 45 s |
Is 72345 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 (72345 ÷ 3 = 24115) | 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 (72345 ÷ 5 = 14469) | 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 (72345 ÷ 7 = 10335) | 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 3) | 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 | No (remainder 9) | 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 72345 a prime number?
No. 72345 = 3 × 5 × 7 × 13 × 53, so it is divisible by 3.
What are the factors of 72345?
1, 3, 5, 7, 13, 15, 21, 35, 39, 53, 65, 91, 105, 159, 195, 265, 273, 371, 455, 689, 795, 1113, 1365, 1855, 2067, 3445, 4823, 5565, 10335, 14469, 24115, 72345.
What is 72345 in binary?
10001101010011001 (hexadecimal 11A99, octal 215231).
What is the square root of 72345?
About 268.9703.
Is 72345 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 72345?
72345 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.