The number 84072
84072 is a composite number with 32 divisors. Its prime factorisation is × 3 × 31 × 113. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 113, 124, 186, 226, 248 … 84072.
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How to work it out
- 1
What is special about 84072: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
84072 is composite. Its prime factorisation is
- 3
The divisors add up to 218880; without 84072 itself that is 134808, so 84072 is abundant (134808 is more than 84072). Euler's totient φ(84072) = 26880 numbers up to 84072 share no factor with it.
- 4
The digits of 84072 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 84072 = 2^{3} \times 3 \times 31 \times 113 \]84072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 218880 |
| Euler totient φ(n) | 26880 |
| Square | 7068101184 |
| Cube | 594229402741248 |
| Square root | 289.951720 (= 2√21018) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 32 |
| Scientific notation | 8.4072 × |
84072 in other forms
| Form | Value |
|---|---|
| In words | eighty-four thousand and seventy-two |
| Binary (base 2) | 10100100001101000 |
| Octal (base 8) | 244150 |
| Hexadecimal (base 16) | 14868 |
| Base 3 | 11021022210 |
| As time | 84072 seconds = 23 h 21 min 12 s |
Is 84072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (84072 ÷ 2 = 42036) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (84072 ÷ 3 = 28024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (84072 ÷ 4 = 21018) | 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 | Yes (84072 ÷ 6 = 14012) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (84072 ÷ 8 = 10509) | 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 2) | 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 | Yes (84072 ÷ 12 = 7006) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 84072 a prime number?
No. 84072 = × 3 × 31 × 113, so it is divisible by 2.
What are the factors of 84072?
1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 113, 124, 186, 226, 248, 339, 372, 452, 678, 744, 904, 1356, 2712, 3503, 7006, 10509, 14012, 21018, 28024, 42036, 84072.
What is 84072 in binary?
10100100001101000 (hexadecimal 14868, octal 244150).
What is the square root of 84072?
About 289.9517, exactly 2√21018.
Is 84072 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 84072?
84072 is a happy number: repeatedly adding the squares of its digits reaches 1.