The number 180
180 is a highly composite number: it has 18 divisors, more than any smaller number. Its prime factorisation is × × 5. Divisors (18): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 180.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 180: a highly composite number: it has 18 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.
- 2
180 is composite. Its prime factorisation is
- 3
The divisors add up to 546; without 180 itself that is 366, so 180 is abundant (366 is more than 180). Euler's totient φ(180) = 48 numbers up to 180 share no factor with it.
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The digits of 180 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 18 steps to reach 1.
LaTeX source of the formulas on this page
\[ 180 = 2^{2} \times 3^{2} \times 5 \]180 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 546 |
| Euler totient φ(n) | 48 |
| Square | 32400 |
| Cube | 5832000 |
| Square root | 13.416408 (= 6√5) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 18 |
| Scientific notation | 1.8 × |
180 in other forms
| Form | Value |
|---|---|
| In words | one hundred and eighty |
| Roman numerals | CLXXX |
| Binary (base 2) | 10110100 |
| Octal (base 8) | 264 |
| Hexadecimal (base 16) | B4 |
| Base 3 | 20200 |
| As time | 180 seconds = 3 min 0 s |
Is 180 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (180 ÷ 2 = 90) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (180 ÷ 3 = 60) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (180 ÷ 4 = 45) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (180 ÷ 5 = 36) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (180 ÷ 6 = 30) | 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 | Yes (180 ÷ 9 = 20) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (180 ÷ 10 = 18) | 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 (180 ÷ 12 = 15) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 180 a prime number?
No. 180 = × × 5, so it is divisible by 2.
What are the factors of 180?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
What is 180 in binary?
10110100 (hexadecimal B4, octal 264).
What is the square root of 180?
About 13.4164, exactly 6√5.
What is 180 in Roman numerals?
CLXXX.
Is 180 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 180?
180 is a highly composite number: it has 18 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.