The number 90
90 is a composite number with 12 divisors. Its prime factorisation is 2 × × 5. Divisors (12): 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90: a Harshad number: divisible by its digit sum 9.
- 2
90 is composite. Its prime factorisation is
- 3
The divisors add up to 234; without 90 itself that is 144, so 90 is abundant (144 is more than 90). Euler's totient φ(90) = 24 numbers up to 90 share no factor with it.
- 4
The digits of 90 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 17 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90 = 2 \times 3^{2} \times 5 \]90 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 234 |
| Euler totient φ(n) | 24 |
| Square | 8100 |
| Cube | 729000 |
| Square root | 9.486833 (= 3√10) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 17 |
| Scientific notation | 9 × |
90 in other forms
| Form | Value |
|---|---|
| In words | ninety |
| Roman numerals | XC |
| Binary (base 2) | 1011010 |
| Octal (base 8) | 132 |
| Hexadecimal (base 16) | 5A |
| Base 3 | 10100 |
| As time | 90 seconds = 1 min 30 s |
Is 90 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90 ÷ 2 = 45) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90 ÷ 3 = 30) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90 ÷ 5 = 18) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90 ÷ 6 = 15) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (90 ÷ 9 = 10) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (90 ÷ 10 = 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90 a prime number?
No. 90 = 2 × × 5, so it is divisible by 2.
What are the factors of 90?
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
What is 90 in binary?
1011010 (hexadecimal 5A, octal 132).
What is the square root of 90?
About 9.4868, exactly 3√10.
What is 90 in Roman numerals?
XC.
Is 90 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 90?
90 is a Harshad number: divisible by its digit sum 9.