The number 4
4 is a highly composite number: it has 3 divisors, more than any smaller number, a power of 2 () and a perfect square (2²). Its prime factorisation is . Divisors (3): 1, 2, 4.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4: a highly composite number: it has 3 divisors, more than any smaller number; a power of 2 (); a perfect square (2²); the square of a prime (2²).
- 2
4 is composite. Its prime factorisation is
- 3
The divisors add up to 7; without 4 itself that is 3, so 4 is deficient (3 is less than 4). Euler's totient φ(4) = 2 numbers up to 4 share no factor with it.
- 4
The digits of 4 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 2 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4 = 2^{2} \]4 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 3 |
| Sum of divisors | 7 |
| Euler totient φ(n) | 2 |
| Square | 16 |
| Cube | 64 |
| Square root | 2 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 2 |
| Scientific notation | 4 × |
| Perfect power |
4 in other forms
| Form | Value |
|---|---|
| In words | four |
| Roman numerals | IV |
| Binary (base 2) | 100 |
| Octal (base 8) | 4 |
| Hexadecimal (base 16) | 4 |
| Base 3 | 11 |
| As time | 4 seconds |
Is 4 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4 ÷ 2 = 2) | 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 (4 ÷ 4 = 1) | 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 | 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 | 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 4) | 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 4 a prime number?
No. 4 = , so it is divisible by 2.
What are the factors of 4?
1, 2, 4.
What is 4 in binary?
100 (hexadecimal 4, octal 4).
What is the square root of 4?
2, because 2 × 2 = 4.
What is 4 in Roman numerals?
IV.
Is 4 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 4?
4 is a highly composite number: it has 3 divisors, more than any smaller number; a power of 2 (); a perfect square (2²); the square of a prime (2²).