The number 105
105 is a triangular number: 1 + 2 + … + 14 = 105. Its prime factorisation is 3 × 5 × 7. Divisors (8): 1, 3, 5, 7, 15, 21, 35, 105.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 105: a triangular number: 1 + 2 + … + 14 = 105.
- 2
105 is composite. Its prime factorisation is
- 3
The divisors add up to 192; without 105 itself that is 87, so 105 is deficient (87 is less than 105). Euler's totient φ(105) = 48 numbers up to 105 share no factor with it.
- 4
The digits of 105 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 105 = 3 \times 5 \times 7 \]
105 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 192 |
| Euler totient φ(n) | 48 |
| Square | 11025 |
| Cube | 1157625 |
| Square root | 10.246951 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 38 |
| Scientific notation | 1.05 × |
105 in other forms
| Form | Value |
|---|---|
| In words | one hundred and five |
| Roman numerals | CV |
| Binary (base 2) | 1101001 |
| Octal (base 8) | 151 |
| Hexadecimal (base 16) | 69 |
| Base 3 | 10220 |
| As time | 105 seconds = 1 min 45 s |
Is 105 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 (105 ÷ 3 = 35) | 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 | Yes (105 ÷ 5 = 21) | 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 | Yes (105 ÷ 7 = 15) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 6) | 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 105 a prime number?
No. 105 = 3 × 5 × 7, so it is divisible by 3.
What are the factors of 105?
1, 3, 5, 7, 15, 21, 35, 105.
What is 105 in binary?
1101001 (hexadecimal 69, octal 151).
What is the square root of 105?
About 10.2470.
What is 105 in Roman numerals?
CV.
Is 105 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 105?
105 is a triangular number: 1 + 2 + … + 14 = 105.