The number 90720
90720 is a composite number with 120 divisors. Its prime factorisation is × × 5 × 7. Divisors (120): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 … 90720.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90720: a Harshad number: divisible by its digit sum 18.
- 2
90720 is composite. Its prime factorisation is
- 3
The divisors add up to 365904; without 90720 itself that is 275184, so 90720 is abundant (275184 is more than 90720). Euler's totient φ(90720) = 20736 numbers up to 90720 share no factor with it.
- 4
The digits of 90720 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 84 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90720 = 2^{5} \times 3^{4} \times 5 \times 7 \]90720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 120 |
| Sum of divisors | 365904 |
| Euler totient φ(n) | 20736 |
| Square | 8230118400 |
| Cube | 746636341248000 |
| Square root | 301.197610 (= 36√70) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 84 |
| Scientific notation | 9.072 × |
90720 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand seven hundred and twenty |
| Binary (base 2) | 10110001001100000 |
| Octal (base 8) | 261140 |
| Hexadecimal (base 16) | 16260 |
| Base 3 | 11121110000 |
| As time | 90720 seconds = 25 h 12 min 0 s |
Is 90720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90720 ÷ 2 = 45360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90720 ÷ 3 = 30240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90720 ÷ 4 = 22680) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90720 ÷ 5 = 18144) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90720 ÷ 6 = 15120) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (90720 ÷ 7 = 12960) | 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 (90720 ÷ 8 = 11340) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (90720 ÷ 9 = 10080) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (90720 ÷ 10 = 9072) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (90720 ÷ 12 = 7560) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90720 a prime number?
No. 90720 = × × 5 × 7, so it is divisible by 2.
What are the factors of 90720?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 81, 84, 90, 96, 105, 108, 112, 120, 126, 135, 140, 144, 160, 162, 168, 180, 189, 210, 216, 224, 240, 252, 270, 280, 288, 315, 324, 336, 360, 378, 405, 420, 432, 480, 504, 540, 560, 567, 630, 648, 672, 720, 756, 810, 840, 864, 945, 1008, 1080, 1120, 1134, 1260, 1296, 1440, 1512, 1620, 1680, 1890, 2016, 2160, 2268, 2520, 2592, 2835, 3024, 3240, 3360, 3780, 4320, 4536, 5040, 5670, 6048, 6480, 7560, 9072, 10080, 11340, 12960, 15120, 18144, 22680, 30240, 45360, 90720.
What is 90720 in binary?
10110001001100000 (hexadecimal 16260, octal 261140).
What is the square root of 90720?
About 301.1976, exactly 36√70.
Is 90720 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 90720?
90720 is a Harshad number: divisible by its digit sum 18.