Number dictionary · Exact arithmetic
4: factors and number facts
four is an even number and is composite. Its 3 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- four
- Roman numeral
- IV
- Prime factorization
- 2^2
- Digital root
- 4
All factors of 4
A positive factor divides 4 with no remainder. In ascending order, the complete list is:
1, 2, 4
Factor pairs
- 1 × 4 = 4
- 2 × 2 = 4
Each pair describes an arrangement of 4 items into equal rows. The 2 × 2 pair is square, so its shared factor appears only once in the factor list.
Divisor totals
- Positive divisors
- 3
- Sum of all divisors
- 7
- Sum excluding 4
- 3
- Classification
- deficient
4 is deficient because its proper divisors add to 3, which is less than 4.
Prime factorization of 4
4 = 2^2
Repeated division, step by step
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
Multiply the prime divisors in these steps to reconstruct 4. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) = 3.
The preceding prime is 3. The next larger prime is 5. The factor list above explains why 4 is composite.
Learn the factorization method4 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four |
| Roman numeral | IV |
| Binary (base 2) | 100 |
| Octal (base 8) | 4 |
| Decimal (base 10) | 4 |
| Hexadecimal (base 16) | 4 |
Check the binary conversion
Read 100 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
4 = 4
Check the hexadecimal conversion
4 × 16^0 = 4
Hexadecimal uses A through F for digit values 10 through 15. These notations represent the same quantity; changing the base does not change the integer.
Square, cube and square root of 4
- 4 squared
- 4 × 4 = 16
- 4 cubed
- 4 × 4 × 4 = 64
- Square root
- = 2
- Simplified radical
- 2
4 is a perfect square: 2 × 2 = 4. It is not a perfect cube.
4 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 4.
Distinguish a square from a square rootMultiplication table for 4
These are the first twelve positive multiples. Unlike the finite factor list, the sequence of multiples continues without an upper limit.
Divisibility checks
| Divide by | Whole quotient | Remainder | Divides exactly? |
|---|---|---|---|
| 2 | 2 | 0 | Yes |
| 3 | 1 | 1 | No |
| 4 | 1 | 0 | Yes |
| 5 | 0 | 4 | No |
| 6 | 0 | 4 | No |
| 7 | 0 | 4 | No |
| 8 | 0 | 4 | No |
| 9 | 0 | 4 | No |
| 10 | 0 | 4 | No |
| 11 | 0 | 4 | No |
| 12 | 0 | 4 | No |
For example, 4 = 7 × 0 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 4
4 contains 1 decimal digit. Its digit sum is 4 = 4.
It already has one digit, so there is no reduction step.
The digital root is 4. 4 reads the same forward and backward, making it a decimal palindrome. Digit patterns depend on the notation being used.
Digital-root arithmetic always finishes at a single digit for a positive integer. Some numerology methods stop at 11, 22 or 33 instead; that is a separate interpretive convention.
Fractions and a worked comparison
As a fraction of 100, 4/100 simplifies to 1/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 0.04.
The greatest common divisor of 4 and 12 is 4. Their least common multiple is 12. The identity GCD × LCM = 4 × 12 = 48 checks both results.
Work through GCF and LCMQuestions about 4
What are the factors of 4?
The positive factors are 1, 2, 4. There are 3 factors, including 1 and 4.
Is 4 a prime number?
No. 4 is composite: 2^2 = 4.
How do you write 4 in Roman numerals?
4 is IV in standard subtractive Roman numeral notation.
What is the binary representation of 4?
4 in decimal is 100 in base 2. Adding its active place values gives 4 = 4.
Methods and reference definitions
Number JD calculates each result from the integer on this page. Positive factors are enumerated in pairs; repeated division gives the prime factorization; place values verify base conversions. Decimal square roots are rounded to six places when irrational.