The number 72084
72084 is a composite number with 12 divisors. Its prime factorisation is × 3 × 6007. Divisors (12): 1, 2, 3, 4, 6, 12, 6007, 12014, 18021, 24028, 36042, 72084.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72084: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
72084 is composite. Its prime factorisation is
- 3
The divisors add up to 168224; without 72084 itself that is 96140, so 72084 is abundant (96140 is more than 72084). Euler's totient φ(72084) = 24024 numbers up to 72084 share no factor with it.
- 4
The digits of 72084 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72084 = 2^{2} \times 3 \times 6007 \]72084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 168224 |
| Euler totient φ(n) | 24024 |
| Square | 5196103056 |
| Cube | 374555892688704 |
| Square root | 268.484636 (= 2√18021) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 42 |
| Scientific notation | 7.2084 × |
72084 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand and eighty-four |
| Binary (base 2) | 10001100110010100 |
| Octal (base 8) | 214624 |
| Hexadecimal (base 16) | 11994 |
| Base 3 | 10122212210 |
| As time | 72084 seconds = 20 h 1 min 24 s |
Is 72084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72084 ÷ 2 = 36042) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72084 ÷ 3 = 24028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72084 ÷ 4 = 18021) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72084 ÷ 6 = 12014) | 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 4) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72084 ÷ 12 = 6007) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72084 a prime number?
No. 72084 = × 3 × 6007, so it is divisible by 2.
What are the factors of 72084?
1, 2, 3, 4, 6, 12, 6007, 12014, 18021, 24028, 36042, 72084.
What is 72084 in binary?
10001100110010100 (hexadecimal 11994, octal 214624).
What is the square root of 72084?
About 268.4846, exactly 2√18021.
Is 72084 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 72084?
72084 is a happy number: repeatedly adding the squares of its digits reaches 1.