Number dictionary · Exact arithmetic
2400: factors and number facts
two thousand four hundred is an even number and is composite. Its 36 positive divisors form 18 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- two thousand four hundred
- Roman numeral
- MMCD
- Prime factorization
- 2^5 × 3 × 5^2
- Digital root
- 6
All factors of 2400
A positive factor divides 2400 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400
Factor pairs
- 1 × 2400 = 2400
- 2 × 1200 = 2400
- 3 × 800 = 2400
- 4 × 600 = 2400
- 5 × 480 = 2400
- 6 × 400 = 2400
- 8 × 300 = 2400
- 10 × 240 = 2400
- 12 × 200 = 2400
- 15 × 160 = 2400
- 16 × 150 = 2400
- 20 × 120 = 2400
- 24 × 100 = 2400
- 25 × 96 = 2400
- 30 × 80 = 2400
- 32 × 75 = 2400
- 40 × 60 = 2400
- 48 × 50 = 2400
Each pair describes an arrangement of 2400 items into equal rows. The pairs have different row and column counts; 2400 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 36
- Sum of all divisors
- 7812
- Sum excluding 2400
- 5412
- Classification
- abundant
2400 is abundant because its proper divisors add to 5412, which is greater than 2400.
Prime factorization of 2400
2400 = 2^5 × 3 × 5^2
Repeated division, step by step
- 2400 ÷ 2 = 1200
- 1200 ÷ 2 = 600
- 600 ÷ 2 = 300
- 300 ÷ 2 = 150
- 150 ÷ 2 = 75
- 75 ÷ 3 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
Multiply the prime divisors in these steps to reconstruct 2400. An exponent records how many times the same prime occurs. The divisor-count calculation is (5 + 1) × (1 + 1) × (2 + 1) = 36.
The preceding prime is 2399. The next larger prime is 2411. The factor list above explains why 2400 is composite.
Learn the factorization method2400 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | two thousand four hundred |
| Roman numeral | MMCD |
| Binary (base 2) | 100101100000 |
| Octal (base 8) | 4540 |
| Decimal (base 10) | 2400 |
| Hexadecimal (base 16) | 960 |
Check the binary conversion
Read 100101100000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
2048 + 256 + 64 + 32 = 2400
Check the hexadecimal conversion
9 × 16^2 + 6 × 16^1 + 0 × 16^0 = 2400
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 2400
- 2400 squared
- 2400 × 2400 = 5,760,000
- 2400 cubed
- 2400 × 2400 × 2400 = 13,824,000,000
- Square root
- ≈ 48.989795
- Simplified radical
- 20√6
2400 lies between 2304 (48²) and 2401 (49²), so it is not a perfect square. It is not a perfect cube.
2400 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 2400.
Distinguish a square from a square rootMultiplication table for 2400
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 | 1200 | 0 | Yes |
| 3 | 800 | 0 | Yes |
| 4 | 600 | 0 | Yes |
| 5 | 480 | 0 | Yes |
| 6 | 400 | 0 | Yes |
| 7 | 342 | 6 | No |
| 8 | 300 | 0 | Yes |
| 9 | 266 | 6 | No |
| 10 | 240 | 0 | Yes |
| 11 | 218 | 2 | No |
| 12 | 200 | 0 | Yes |
For example, 2400 = 7 × 342 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 2400
2400 contains 4 decimal digits. Its digit sum is 2 + 4 + 0 + 0 = 6.
- 2400: 2 + 4 + 0 + 0 = 6
The digital root is 6. Reversing its digits gives 0042; 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, 2400/100 simplifies to 24/1 by dividing both terms by their greatest common divisor, 100. Its decimal value is 24. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 2400 and 12 is 12. Their least common multiple is 2400. The identity GCD × LCM = 2400 × 12 = 28800 checks both results.
Work through GCF and LCMQuestions about 2400
What are the factors of 2400?
The positive factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400. There are 36 factors, including 1 and 2400.
Is 2400 a prime number?
No. 2400 is composite: 2^5 × 3 × 5^2 = 2400.
How do you write 2400 in Roman numerals?
2400 is MMCD in standard subtractive Roman numeral notation.
What is the binary representation of 2400?
2400 in decimal is 100101100000 in base 2. Adding its active place values gives 2048 + 256 + 64 + 32 = 2400.
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 2400
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 2400 add to 6. 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.