Number dictionary · Exact arithmetic
400: factors and number facts
four hundred is an even number and is composite. Its 15 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- four hundred
- Roman numeral
- CD
- Prime factorization
- 2^4 × 5^2
- Digital root
- 4
All factors of 400
A positive factor divides 400 with no remainder. In ascending order, the complete list is:
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Factor pairs
- 1 × 400 = 400
- 2 × 200 = 400
- 4 × 100 = 400
- 5 × 80 = 400
- 8 × 50 = 400
- 10 × 40 = 400
- 16 × 25 = 400
- 20 × 20 = 400
Each pair describes an arrangement of 400 items into equal rows. The 20 × 20 pair is square, so its shared factor appears only once in the factor list.
Divisor totals
- Positive divisors
- 15
- Sum of all divisors
- 961
- Sum excluding 400
- 561
- Classification
- abundant
400 is abundant because its proper divisors add to 561, which is greater than 400.
Prime factorization of 400
400 = 2^4 × 5^2
Repeated division, step by step
- 400 ÷ 2 = 200
- 200 ÷ 2 = 100
- 100 ÷ 2 = 50
- 50 ÷ 2 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
Multiply the prime divisors in these steps to reconstruct 400. An exponent records how many times the same prime occurs. The divisor-count calculation is (4 + 1) × (2 + 1) = 15.
The preceding prime is 397. The next larger prime is 401. The factor list above explains why 400 is composite.
Learn the factorization method400 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred |
| Roman numeral | CD |
| Binary (base 2) | 110010000 |
| Octal (base 8) | 620 |
| Decimal (base 10) | 400 |
| Hexadecimal (base 16) | 190 |
Check the binary conversion
Read 110010000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 128 + 16 = 400
Check the hexadecimal conversion
1 × 16^2 + 9 × 16^1 + 0 × 16^0 = 400
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 400
- 400 squared
- 400 × 400 = 160,000
- 400 cubed
- 400 × 400 × 400 = 64,000,000
- Square root
- = 20
- Simplified radical
- 20
400 is a perfect square: 20 × 20 = 400. It is not a perfect cube.
400 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 400.
Distinguish a square from a square rootMultiplication table for 400
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 | 200 | 0 | Yes |
| 3 | 133 | 1 | No |
| 4 | 100 | 0 | Yes |
| 5 | 80 | 0 | Yes |
| 6 | 66 | 4 | No |
| 7 | 57 | 1 | No |
| 8 | 50 | 0 | Yes |
| 9 | 44 | 4 | No |
| 10 | 40 | 0 | Yes |
| 11 | 36 | 4 | No |
| 12 | 33 | 4 | No |
For example, 400 = 7 × 57 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 400
400 contains 3 decimal digits. Its digit sum is 4 + 0 + 0 = 4.
- 400: 4 + 0 + 0 = 4
The digital root is 4. Reversing its digits gives 004; it is not 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, 400/100 simplifies to 4/1 by dividing both terms by their greatest common divisor, 100. Its decimal value is 4. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 400 and 12 is 4. Their least common multiple is 1200. The identity GCD × LCM = 400 × 12 = 4800 checks both results.
Work through GCF and LCMQuestions about 400
What are the factors of 400?
The positive factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. There are 15 factors, including 1 and 400.
Is 400 a prime number?
No. 400 is composite: 2^4 × 5^2 = 400.
How do you write 400 in Roman numerals?
400 is CD in standard subtractive Roman numeral notation.
What is the binary representation of 400?
400 in decimal is 110010000 in base 2. Adding its active place values gives 256 + 128 + 16 = 400.
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.
NUMBER JOURNAL / JD
A reflective note on 400
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 400 add to 4. That arithmetic result is separate from the cultural symbolism of the pattern. If this number matters to you, write down what you noticed and choose one grounded action rather than treating the sighting as a prediction.