The number 117
117 is a composite number with 6 divisors. Its prime factorisation is × 13. Divisors (6): 1, 3, 9, 13, 39, 117.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 117: a Harshad number: divisible by its digit sum 9.
- 2
117 is composite. Its prime factorisation is
- 3
The divisors add up to 182; without 117 itself that is 65, so 117 is deficient (65 is less than 117). Euler's totient φ(117) = 72 numbers up to 117 share no factor with it.
- 4
The digits of 117 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 20 steps to reach 1.
LaTeX source of the formulas on this page
\[ 117 = 3^{2} \times 13 \]117 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 182 |
| Euler totient φ(n) | 72 |
| Square | 13689 |
| Cube | 1601613 |
| Square root | 10.816654 (= 3√13) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 20 |
| Scientific notation | 1.17 × |
117 in other forms
| Form | Value |
|---|---|
| In words | one hundred and seventeen |
| Roman numerals | CXVII |
| Binary (base 2) | 1110101 |
| Octal (base 8) | 165 |
| Hexadecimal (base 16) | 75 |
| Base 3 | 11100 |
| As time | 117 seconds = 1 min 57 s |
Is 117 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 (117 ÷ 3 = 39) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 | No (remainder 3) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (117 ÷ 9 = 13) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 117 a prime number?
No. 117 = × 13, so it is divisible by 3.
What are the factors of 117?
1, 3, 9, 13, 39, 117.
What is 117 in binary?
1110101 (hexadecimal 75, octal 165).
What is the square root of 117?
About 10.8167, exactly 3√13.
What is 117 in Roman numerals?
CXVII.
Is 117 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 117?
117 is a Harshad number: divisible by its digit sum 9.