Number dictionary · Exact arithmetic
488: factors and number facts
four hundred eighty-eight is an even number and is composite. Its 8 positive divisors form 4 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- four hundred eighty-eight
- Roman numeral
- CDLXXXVIII
- Prime factorization
- 2^3 × 61
- Digital root
- 2
All factors of 488
A positive factor divides 488 with no remainder. In ascending order, the complete list is:
1, 2, 4, 8, 61, 122, 244, 488
Factor pairs
- 1 × 488 = 488
- 2 × 244 = 488
- 4 × 122 = 488
- 8 × 61 = 488
Each pair describes an arrangement of 488 items into equal rows. The pairs have different row and column counts; 488 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 930
- Sum excluding 488
- 442
- Classification
- deficient
488 is deficient because its proper divisors add to 442, which is less than 488.
Prime factorization of 488
488 = 2^3 × 61
Repeated division, step by step
- 488 ÷ 2 = 244
- 244 ÷ 2 = 122
- 122 ÷ 2 = 61
- 61 ÷ 61 = 1
Multiply the prime divisors in these steps to reconstruct 488. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) = 8.
The preceding prime is 487. The next larger prime is 491. The factor list above explains why 488 is composite.
Learn the factorization method488 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred eighty-eight |
| Roman numeral | CDLXXXVIII |
| Binary (base 2) | 111101000 |
| Octal (base 8) | 750 |
| Decimal (base 10) | 488 |
| Hexadecimal (base 16) | 1E8 |
Check the binary conversion
Read 111101000 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 + 8 = 488
Check the hexadecimal conversion
1 × 16^2 + 14 × 16^1 + 8 × 16^0 = 488
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 488
- 488 squared
- 488 × 488 = 238,144
- 488 cubed
- 488 × 488 × 488 = 116,214,272
- Square root
- ≈ 22.090722
- Simplified radical
- 2√122
488 lies between 484 (22²) and 529 (23²), so it is not a perfect square. It is not a perfect cube.
488 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 488.
Distinguish a square from a square rootMultiplication table for 488
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 | 244 | 0 | Yes |
| 3 | 162 | 2 | No |
| 4 | 122 | 0 | Yes |
| 5 | 97 | 3 | No |
| 6 | 81 | 2 | No |
| 7 | 69 | 5 | No |
| 8 | 61 | 0 | Yes |
| 9 | 54 | 2 | No |
| 10 | 48 | 8 | No |
| 11 | 44 | 4 | No |
| 12 | 40 | 8 | No |
For example, 488 = 7 × 69 + 5. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 488
488 contains 3 decimal digits. Its digit sum is 4 + 8 + 8 = 20.
- 488: 4 + 8 + 8 = 20
- 20: 2 + 0 = 2
The digital root is 2. Reversing its digits gives 884; 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, 488/100 simplifies to 122/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 4.88. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 488 and 12 is 4. Their least common multiple is 1464. The identity GCD × LCM = 488 × 12 = 5856 checks both results.
Work through GCF and LCMQuestions about 488
What are the factors of 488?
The positive factors are 1, 2, 4, 8, 61, 122, 244, 488. There are 8 factors, including 1 and 488.
Is 488 a prime number?
No. 488 is composite: 2^3 × 61 = 488.
How do you write 488 in Roman numerals?
488 is CDLXXXVIII in standard subtractive Roman numeral notation.
What is the binary representation of 488?
488 in decimal is 111101000 in base 2. Adding its active place values gives 256 + 128 + 64 + 32 + 8 = 488.
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 488
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 488 add to 20. 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.