The number 644
644 is a composite number with 12 divisors. Its prime factorisation is × 7 × 23. Divisors (12): 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 644: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 14.
- 2
644 is composite. Its prime factorisation is
- 3
The divisors add up to 1344; without 644 itself that is 700, so 644 is abundant (700 is more than 644). Euler's totient φ(644) = 264 numbers up to 644 share no factor with it.
- 4
The digits of 644 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 100 steps to reach 1.
LaTeX source of the formulas on this page
\[ 644 = 2^{2} \times 7 \times 23 \]644 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1344 |
| Euler totient φ(n) | 264 |
| Square | 414736 |
| Cube | 267089984 |
| Square root | 25.377155 (= 2√161) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 100 |
| Scientific notation | 6.44 × |
644 in other forms
| Form | Value |
|---|---|
| In words | six hundred and forty-four |
| Roman numerals | DCXLIV |
| Binary (base 2) | 1010000100 |
| Octal (base 8) | 1204 |
| Hexadecimal (base 16) | 284 |
| Base 3 | 212212 |
| As time | 644 seconds = 10 min 44 s |
Is 644 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (644 ÷ 2 = 322) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (644 ÷ 4 = 161) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (644 ÷ 7 = 92) | 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 5) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 644 a prime number?
No. 644 = × 7 × 23, so it is divisible by 2.
What are the factors of 644?
1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644.
What is 644 in binary?
1010000100 (hexadecimal 284, octal 1204).
What is the square root of 644?
About 25.3772, exactly 2√161.
What is 644 in Roman numerals?
DCXLIV.
Is 644 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 644?
644 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 14.