Number dictionary · Exact arithmetic
480: factors and number facts
four hundred eighty is an even number and is composite. Its 24 positive divisors form 12 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- four hundred eighty
- Roman numeral
- CDLXXX
- Prime factorization
- 2^5 × 3 × 5
- Digital root
- 3
All factors of 480
A positive factor divides 480 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480
Factor pairs
- 1 × 480 = 480
- 2 × 240 = 480
- 3 × 160 = 480
- 4 × 120 = 480
- 5 × 96 = 480
- 6 × 80 = 480
- 8 × 60 = 480
- 10 × 48 = 480
- 12 × 40 = 480
- 15 × 32 = 480
- 16 × 30 = 480
- 20 × 24 = 480
Each pair describes an arrangement of 480 items into equal rows. The pairs have different row and column counts; 480 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 24
- Sum of all divisors
- 1512
- Sum excluding 480
- 1032
- Classification
- abundant
480 is abundant because its proper divisors add to 1032, which is greater than 480.
Prime factorization of 480
480 = 2^5 × 3 × 5
Repeated division, step by step
- 480 ÷ 2 = 240
- 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 480. An exponent records how many times the same prime occurs. The divisor-count calculation is (5 + 1) × (1 + 1) × (1 + 1) = 24.
The preceding prime is 479. The next larger prime is 487. The factor list above explains why 480 is composite.
Learn the factorization method480 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred eighty |
| Roman numeral | CDLXXX |
| Binary (base 2) | 111100000 |
| Octal (base 8) | 740 |
| Decimal (base 10) | 480 |
| Hexadecimal (base 16) | 1E0 |
Check the binary conversion
Read 111100000 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 + 64 + 32 = 480
Check the hexadecimal conversion
1 × 16^2 + 14 × 16^1 + 0 × 16^0 = 480
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 480
- 480 squared
- 480 × 480 = 230,400
- 480 cubed
- 480 × 480 × 480 = 110,592,000
- Square root
- ≈ 21.908902
- Simplified radical
- 4√30
480 lies between 441 (21²) and 484 (22²), so it is not a perfect square. It is not a perfect cube.
480 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 480.
Distinguish a square from a square rootMultiplication table for 480
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 | 240 | 0 | Yes |
| 3 | 160 | 0 | Yes |
| 4 | 120 | 0 | Yes |
| 5 | 96 | 0 | Yes |
| 6 | 80 | 0 | Yes |
| 7 | 68 | 4 | No |
| 8 | 60 | 0 | Yes |
| 9 | 53 | 3 | No |
| 10 | 48 | 0 | Yes |
| 11 | 43 | 7 | No |
| 12 | 40 | 0 | Yes |
For example, 480 = 7 × 68 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 480
480 contains 3 decimal digits. Its digit sum is 4 + 8 + 0 = 12.
- 480: 4 + 8 + 0 = 12
- 12: 1 + 2 = 3
The digital root is 3. Reversing its digits gives 084; 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, 480/100 simplifies to 24/5 by dividing both terms by their greatest common divisor, 20. Its decimal value is 4.8. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 480 and 12 is 12. Their least common multiple is 480. The identity GCD × LCM = 480 × 12 = 5760 checks both results.
Work through GCF and LCMQuestions about 480
What are the factors of 480?
The positive factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480. There are 24 factors, including 1 and 480.
Is 480 a prime number?
No. 480 is composite: 2^5 × 3 × 5 = 480.
How do you write 480 in Roman numerals?
480 is CDLXXX in standard subtractive Roman numeral notation.
What is the binary representation of 480?
480 in decimal is 111100000 in base 2. Adding its active place values gives 256 + 128 + 64 + 32 = 480.
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 480
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 480 add to 12. 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.