The number 135
135 is a composite number with 8 divisors. Its prime factorisation is × 5. Divisors (8): 1, 3, 5, 9, 15, 27, 45, 135.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 135: a Harshad number: divisible by its digit sum 9.
- 2
135 is composite. Its prime factorisation is
- 3
The divisors add up to 240; without 135 itself that is 105, so 135 is deficient (105 is less than 135). Euler's totient φ(135) = 72 numbers up to 135 share no factor with it.
- 4
The digits of 135 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 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 135 = 3^{3} \times 5 \]135 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 240 |
| Euler totient φ(n) | 72 |
| Square | 18225 |
| Cube | 2460375 |
| Square root | 11.618950 (= 3√15) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 41 |
| Scientific notation | 1.35 × |
135 in other forms
| Form | Value |
|---|---|
| In words | one hundred and thirty-five |
| Roman numerals | CXXXV |
| Binary (base 2) | 10000111 |
| Octal (base 8) | 207 |
| Hexadecimal (base 16) | 87 |
| Base 3 | 12000 |
| As time | 135 seconds = 2 min 15 s |
Is 135 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (135 ÷ 3 = 45) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (135 ÷ 5 = 27) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 | No (remainder 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (135 ÷ 9 = 15) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | 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 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 135 a prime number?
No. 135 = × 5, so it is divisible by 3.
What are the factors of 135?
1, 3, 5, 9, 15, 27, 45, 135.
What is 135 in binary?
10000111 (hexadecimal 87, octal 207).
What is the square root of 135?
About 11.6190, exactly 3√15.
What is 135 in Roman numerals?
CXXXV.
Is 135 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 135?
135 is a Harshad number: divisible by its digit sum 9.