The number 312
312 is a composite number with 16 divisors. Its prime factorisation is × 3 × 13. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 312: a Harshad number: divisible by its digit sum 6.
- 2
312 is composite. Its prime factorisation is
- 3
The divisors add up to 840; without 312 itself that is 528, so 312 is abundant (528 is more than 312). Euler's totient φ(312) = 96 numbers up to 312 share no factor with it.
- 4
The digits of 312 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 312 = 2^{3} \times 3 \times 13 \]312 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 840 |
| Euler totient φ(n) | 96 |
| Square | 97344 |
| Cube | 30371328 |
| Square root | 17.663522 (= 2√78) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 37 |
| Scientific notation | 3.12 × |
312 in other forms
| Form | Value |
|---|---|
| In words | three hundred and twelve |
| Roman numerals | CCCXII |
| Binary (base 2) | 100111000 |
| Octal (base 8) | 470 |
| Hexadecimal (base 16) | 138 |
| Base 3 | 102120 |
| As time | 312 seconds = 5 min 12 s |
Is 312 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (312 ÷ 2 = 156) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (312 ÷ 3 = 104) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (312 ÷ 4 = 78) | 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 | Yes (312 ÷ 6 = 52) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | Yes (312 ÷ 8 = 39) | 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 2) | 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 (312 ÷ 12 = 26) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 312 a prime number?
No. 312 = × 3 × 13, so it is divisible by 2.
What are the factors of 312?
1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.
What is 312 in binary?
100111000 (hexadecimal 138, octal 470).
What is the square root of 312?
About 17.6635, exactly 2√78.
What is 312 in Roman numerals?
CCCXII.
Is 312 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 312?
312 is a Harshad number: divisible by its digit sum 6.