The number 315
315 is a composite number with 12 divisors. Its prime factorisation is × 5 × 7. Divisors (12): 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 315: a Harshad number: divisible by its digit sum 9.
- 2
315 is composite. Its prime factorisation is
- 3
The divisors add up to 624; without 315 itself that is 309, so 315 is deficient (309 is less than 315). Euler's totient φ(315) = 144 numbers up to 315 share no factor with it.
- 4
The digits of 315 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 315 = 3^{2} \times 5 \times 7 \]315 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 624 |
| Euler totient φ(n) | 144 |
| Square | 99225 |
| Cube | 31255875 |
| Square root | 17.748239 (= 3√35) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 37 |
| Scientific notation | 3.15 × |
315 in other forms
| Form | Value |
|---|---|
| In words | three hundred and fifteen |
| Roman numerals | CCCXV |
| Binary (base 2) | 100111011 |
| Octal (base 8) | 473 |
| Hexadecimal (base 16) | 13B |
| Base 3 | 102200 |
| As time | 315 seconds = 5 min 15 s |
Is 315 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 (315 ÷ 3 = 105) | 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 (315 ÷ 5 = 63) | 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 (315 ÷ 7 = 45) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (315 ÷ 9 = 35) | 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 7) | 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 315 a prime number?
No. 315 = × 5 × 7, so it is divisible by 3.
What are the factors of 315?
1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
What is 315 in binary?
100111011 (hexadecimal 13B, octal 473).
What is the square root of 315?
About 17.7482, exactly 3√35.
What is 315 in Roman numerals?
CCCXV.
Is 315 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 315?
315 is a Harshad number: divisible by its digit sum 9.