The number 90072
90072 is a composite number with 40 divisors. Its prime factorisation is × × 139. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108 … 90072.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90072: a Harshad number: divisible by its digit sum 18.
- 2
90072 is composite. Its prime factorisation is
- 3
The divisors add up to 254100; without 90072 itself that is 164028, so 90072 is abundant (164028 is more than 90072). Euler's totient φ(90072) = 29808 numbers up to 90072 share no factor with it.
- 4
The digits of 90072 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90072 = 2^{3} \times 3^{4} \times 139 \]90072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 254100 |
| Euler totient φ(n) | 29808 |
| Square | 8112965184 |
| Cube | 730751000053248 |
| Square root | 300.119976 (= 18√278) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 63 |
| Scientific notation | 9.0072 × |
90072 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand and seventy-two |
| Binary (base 2) | 10101111111011000 |
| Octal (base 8) | 257730 |
| Hexadecimal (base 16) | 15FD8 |
| Base 3 | 11120120000 |
| As time | 90072 seconds = 25 h 1 min 12 s |
Is 90072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90072 ÷ 2 = 45036) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90072 ÷ 3 = 30024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90072 ÷ 4 = 22518) | 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 (90072 ÷ 6 = 15012) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (90072 ÷ 8 = 11259) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (90072 ÷ 9 = 10008) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (90072 ÷ 12 = 7506) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90072 a prime number?
No. 90072 = × × 139, so it is divisible by 2.
What are the factors of 90072?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 139, 162, 216, 278, 324, 417, 556, 648, 834, 1112, 1251, 1668, 2502, 3336, 3753, 5004, 7506, 10008, 11259, 15012, 22518, 30024, 45036, 90072.
What is 90072 in binary?
10101111111011000 (hexadecimal 15FD8, octal 257730).
What is the square root of 90072?
About 300.1200, exactly 18√278.
Is 90072 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 90072?
90072 is a Harshad number: divisible by its digit sum 18.