The number 364
364 is a composite number with 12 divisors. Its prime factorisation is × 7 × 13. Divisors (12): 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 364: a Harshad number: divisible by its digit sum 13.
- 2
364 is composite. Its prime factorisation is
- 3
The divisors add up to 784; without 364 itself that is 420, so 364 is abundant (420 is more than 364). Euler's totient φ(364) = 144 numbers up to 364 share no factor with it.
- 4
The digits of 364 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 364 = 2^{2} \times 7 \times 13 \]364 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 784 |
| Euler totient φ(n) | 144 |
| Square | 132496 |
| Cube | 48228544 |
| Square root | 19.078784 (= 2√91) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 94 |
| Scientific notation | 3.64 × |
364 in other forms
| Form | Value |
|---|---|
| In words | three hundred and sixty-four |
| Roman numerals | CCCLXIV |
| Binary (base 2) | 101101100 |
| Octal (base 8) | 554 |
| Hexadecimal (base 16) | 16C |
| Base 3 | 111111 |
| As time | 364 seconds = 6 min 4 s |
Is 364 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (364 ÷ 2 = 182) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (364 ÷ 4 = 91) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (364 ÷ 7 = 52) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 364 a prime number?
No. 364 = × 7 × 13, so it is divisible by 2.
What are the factors of 364?
1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.
What is 364 in binary?
101101100 (hexadecimal 16C, octal 554).
What is the square root of 364?
About 19.0788, exactly 2√91.
What is 364 in Roman numerals?
CCCLXIV.
Is 364 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 364?
364 is a Harshad number: divisible by its digit sum 13.