Number dictionary · Exact arithmetic
240: factors and number facts
two hundred forty is an even number and is composite. Its 20 positive divisors form 10 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- two hundred forty
- Roman numeral
- CCXL
- Prime factorization
- 2^4 × 3 × 5
- Digital root
- 6
All factors of 240
A positive factor divides 240 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
Factor pairs
- 1 × 240 = 240
- 2 × 120 = 240
- 3 × 80 = 240
- 4 × 60 = 240
- 5 × 48 = 240
- 6 × 40 = 240
- 8 × 30 = 240
- 10 × 24 = 240
- 12 × 20 = 240
- 15 × 16 = 240
Each pair describes an arrangement of 240 items into equal rows. The pairs have different row and column counts; 240 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 20
- Sum of all divisors
- 744
- Sum excluding 240
- 504
- Classification
- abundant
240 is abundant because its proper divisors add to 504, which is greater than 240.
Prime factorization of 240
240 = 2^4 × 3 × 5
Repeated division, step by step
- 240 ÷ 2 = 120
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
Multiply the prime divisors in these steps to reconstruct 240. An exponent records how many times the same prime occurs. The divisor-count calculation is (4 + 1) × (1 + 1) × (1 + 1) = 20.
The preceding prime is 239. The next larger prime is 241. The factor list above explains why 240 is composite.
Learn the factorization method240 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | two hundred forty |
| Roman numeral | CCXL |
| Binary (base 2) | 11110000 |
| Octal (base 8) | 360 |
| Decimal (base 10) | 240 |
| Hexadecimal (base 16) | F0 |
Check the binary conversion
Read 11110000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
128 + 64 + 32 + 16 = 240
Check the hexadecimal conversion
15 × 16^1 + 0 × 16^0 = 240
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 240
- 240 squared
- 240 × 240 = 57,600
- 240 cubed
- 240 × 240 × 240 = 13,824,000
- Square root
- ≈ 15.491933
- Simplified radical
- 4√15
240 lies between 225 (15²) and 256 (16²), so it is not a perfect square. It is not a perfect cube.
240 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 240.
Distinguish a square from a square rootMultiplication table for 240
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 | 120 | 0 | Yes |
| 3 | 80 | 0 | Yes |
| 4 | 60 | 0 | Yes |
| 5 | 48 | 0 | Yes |
| 6 | 40 | 0 | Yes |
| 7 | 34 | 2 | No |
| 8 | 30 | 0 | Yes |
| 9 | 26 | 6 | No |
| 10 | 24 | 0 | Yes |
| 11 | 21 | 9 | No |
| 12 | 20 | 0 | Yes |
For example, 240 = 7 × 34 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 240
240 contains 3 decimal digits. Its digit sum is 2 + 4 + 0 = 6.
- 240: 2 + 4 + 0 = 6
The digital root is 6. Reversing its digits gives 042; 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, 240/100 simplifies to 12/5 by dividing both terms by their greatest common divisor, 20. Its decimal value is 2.4. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 240 and 12 is 12. Their least common multiple is 240. The identity GCD × LCM = 240 × 12 = 2880 checks both results.
Work through GCF and LCMQuestions about 240
What are the factors of 240?
The positive factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240. There are 20 factors, including 1 and 240.
Is 240 a prime number?
No. 240 is composite: 2^4 × 3 × 5 = 240.
How do you write 240 in Roman numerals?
240 is CCXL in standard subtractive Roman numeral notation.
What is the binary representation of 240?
240 in decimal is 11110000 in base 2. Adding its active place values gives 128 + 64 + 32 + 16 = 240.
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 240
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 240 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.