Number dictionary · Exact arithmetic
248: factors and number facts
two hundred forty-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
- two hundred forty-eight
- Roman numeral
- CCXLVIII
- Prime factorization
- 2^3 × 31
- Digital root
- 5
All factors of 248
A positive factor divides 248 with no remainder. In ascending order, the complete list is:
1, 2, 4, 8, 31, 62, 124, 248
Factor pairs
- 1 × 248 = 248
- 2 × 124 = 248
- 4 × 62 = 248
- 8 × 31 = 248
Each pair describes an arrangement of 248 items into equal rows. The pairs have different row and column counts; 248 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 480
- Sum excluding 248
- 232
- Classification
- deficient
248 is deficient because its proper divisors add to 232, which is less than 248.
Prime factorization of 248
248 = 2^3 × 31
Repeated division, step by step
- 248 ÷ 2 = 124
- 124 ÷ 2 = 62
- 62 ÷ 2 = 31
- 31 ÷ 31 = 1
Multiply the prime divisors in these steps to reconstruct 248. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) = 8.
The preceding prime is 241. The next larger prime is 251. The factor list above explains why 248 is composite.
Learn the factorization method248 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | two hundred forty-eight |
| Roman numeral | CCXLVIII |
| Binary (base 2) | 11111000 |
| Octal (base 8) | 370 |
| Decimal (base 10) | 248 |
| Hexadecimal (base 16) | F8 |
Check the binary conversion
Read 11111000 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 + 8 = 248
Check the hexadecimal conversion
15 × 16^1 + 8 × 16^0 = 248
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 248
- 248 squared
- 248 × 248 = 61,504
- 248 cubed
- 248 × 248 × 248 = 15,252,992
- Square root
- ≈ 15.748016
- Simplified radical
- 2√62
248 lies between 225 (15²) and 256 (16²), so it is not a perfect square. It is not a perfect cube.
248 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 248.
Distinguish a square from a square rootMultiplication table for 248
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 | 124 | 0 | Yes |
| 3 | 82 | 2 | No |
| 4 | 62 | 0 | Yes |
| 5 | 49 | 3 | No |
| 6 | 41 | 2 | No |
| 7 | 35 | 3 | No |
| 8 | 31 | 0 | Yes |
| 9 | 27 | 5 | No |
| 10 | 24 | 8 | No |
| 11 | 22 | 6 | No |
| 12 | 20 | 8 | No |
For example, 248 = 7 × 35 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 248
248 contains 3 decimal digits. Its digit sum is 2 + 4 + 8 = 14.
- 248: 2 + 4 + 8 = 14
- 14: 1 + 4 = 5
The digital root is 5. Reversing its digits gives 842; 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, 248/100 simplifies to 62/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 2.48. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 248 and 12 is 4. Their least common multiple is 744. The identity GCD × LCM = 248 × 12 = 2976 checks both results.
Work through GCF and LCMQuestions about 248
What are the factors of 248?
The positive factors are 1, 2, 4, 8, 31, 62, 124, 248. There are 8 factors, including 1 and 248.
Is 248 a prime number?
No. 248 is composite: 2^3 × 31 = 248.
How do you write 248 in Roman numerals?
248 is CCXLVIII in standard subtractive Roman numeral notation.
What is the binary representation of 248?
248 in decimal is 11111000 in base 2. Adding its active place values gives 128 + 64 + 32 + 16 + 8 = 248.
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 248
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 248 add to 14. 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.