Number dictionary · Exact arithmetic
48: factors and number facts
forty-eight is an even number and is composite. Its 10 positive divisors form 5 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- forty-eight
- Roman numeral
- XLVIII
- Prime factorization
- 2^4 × 3
- Digital root
- 3
All factors of 48
A positive factor divides 48 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factor pairs
- 1 × 48 = 48
- 2 × 24 = 48
- 3 × 16 = 48
- 4 × 12 = 48
- 6 × 8 = 48
Each pair describes an arrangement of 48 items into equal rows. The pairs have different row and column counts; 48 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 10
- Sum of all divisors
- 124
- Sum excluding 48
- 76
- Classification
- abundant
48 is abundant because its proper divisors add to 76, which is greater than 48.
Prime factorization of 48
48 = 2^4 × 3
Repeated division, step by step
- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 ÷ 3 = 1
Multiply the prime divisors in these steps to reconstruct 48. An exponent records how many times the same prime occurs. The divisor-count calculation is (4 + 1) × (1 + 1) = 10.
The preceding prime is 47. The next larger prime is 53. The factor list above explains why 48 is composite.
Learn the factorization method48 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | forty-eight |
| Roman numeral | XLVIII |
| Binary (base 2) | 110000 |
| Octal (base 8) | 60 |
| Decimal (base 10) | 48 |
| Hexadecimal (base 16) | 30 |
Check the binary conversion
Read 110000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
32 + 16 = 48
Check the hexadecimal conversion
3 × 16^1 + 0 × 16^0 = 48
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 48
- 48 squared
- 48 × 48 = 2,304
- 48 cubed
- 48 × 48 × 48 = 110,592
- Square root
- ≈ 6.928203
- Simplified radical
- 4√3
48 lies between 36 (6²) and 49 (7²), so it is not a perfect square. It is not a perfect cube.
48 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 48.
Distinguish a square from a square rootMultiplication table for 48
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 | 24 | 0 | Yes |
| 3 | 16 | 0 | Yes |
| 4 | 12 | 0 | Yes |
| 5 | 9 | 3 | No |
| 6 | 8 | 0 | Yes |
| 7 | 6 | 6 | No |
| 8 | 6 | 0 | Yes |
| 9 | 5 | 3 | No |
| 10 | 4 | 8 | No |
| 11 | 4 | 4 | No |
| 12 | 4 | 0 | Yes |
For example, 48 = 7 × 6 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 48
48 contains 2 decimal digits. Its digit sum is 4 + 8 = 12.
- 48: 4 + 8 = 12
- 12: 1 + 2 = 3
The digital root is 3. Reversing its digits gives 84; 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, 48/100 simplifies to 12/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 0.48.
The greatest common divisor of 48 and 12 is 12. Their least common multiple is 48. The identity GCD × LCM = 48 × 12 = 576 checks both results.
Work through GCF and LCMQuestions about 48
What are the factors of 48?
The positive factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 factors, including 1 and 48.
Is 48 a prime number?
No. 48 is composite: 2^4 × 3 = 48.
How do you write 48 in Roman numerals?
48 is XLVIII in standard subtractive Roman numeral notation.
What is the binary representation of 48?
48 in decimal is 110000 in base 2. Adding its active place values gives 32 + 16 = 48.
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 48
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 48 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.