Number dictionary · Exact arithmetic
448: factors and number facts
four hundred forty-eight is an even number and is composite. Its 14 positive divisors form 7 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- four hundred forty-eight
- Roman numeral
- CDXLVIII
- Prime factorization
- 2^6 × 7
- Digital root
- 7
All factors of 448
A positive factor divides 448 with no remainder. In ascending order, the complete list is:
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448
Factor pairs
- 1 × 448 = 448
- 2 × 224 = 448
- 4 × 112 = 448
- 7 × 64 = 448
- 8 × 56 = 448
- 14 × 32 = 448
- 16 × 28 = 448
Each pair describes an arrangement of 448 items into equal rows. The pairs have different row and column counts; 448 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 14
- Sum of all divisors
- 1016
- Sum excluding 448
- 568
- Classification
- abundant
448 is abundant because its proper divisors add to 568, which is greater than 448.
Prime factorization of 448
448 = 2^6 × 7
Repeated division, step by step
- 448 ÷ 2 = 224
- 224 ÷ 2 = 112
- 112 ÷ 2 = 56
- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 448. An exponent records how many times the same prime occurs. The divisor-count calculation is (6 + 1) × (1 + 1) = 14.
The preceding prime is 443. The next larger prime is 449. The factor list above explains why 448 is composite.
Learn the factorization method448 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred forty-eight |
| Roman numeral | CDXLVIII |
| Binary (base 2) | 111000000 |
| Octal (base 8) | 700 |
| Decimal (base 10) | 448 |
| Hexadecimal (base 16) | 1C0 |
Check the binary conversion
Read 111000000 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 = 448
Check the hexadecimal conversion
1 × 16^2 + 12 × 16^1 + 0 × 16^0 = 448
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 448
- 448 squared
- 448 × 448 = 200,704
- 448 cubed
- 448 × 448 × 448 = 89,915,392
- Square root
- ≈ 21.166010
- Simplified radical
- 8√7
448 lies between 441 (21²) and 484 (22²), so it is not a perfect square. It is not a perfect cube.
448 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 448.
Distinguish a square from a square rootMultiplication table for 448
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 | 224 | 0 | Yes |
| 3 | 149 | 1 | No |
| 4 | 112 | 0 | Yes |
| 5 | 89 | 3 | No |
| 6 | 74 | 4 | No |
| 7 | 64 | 0 | Yes |
| 8 | 56 | 0 | Yes |
| 9 | 49 | 7 | No |
| 10 | 44 | 8 | No |
| 11 | 40 | 8 | No |
| 12 | 37 | 4 | No |
For example, 448 = 7 × 64 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 448
448 contains 3 decimal digits. Its digit sum is 4 + 4 + 8 = 16.
- 448: 4 + 4 + 8 = 16
- 16: 1 + 6 = 7
The digital root is 7. Reversing its digits gives 844; 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, 448/100 simplifies to 112/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 4.48. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 448 and 12 is 4. Their least common multiple is 1344. The identity GCD × LCM = 448 × 12 = 5376 checks both results.
Work through GCF and LCMQuestions about 448
What are the factors of 448?
The positive factors are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448. There are 14 factors, including 1 and 448.
Is 448 a prime number?
No. 448 is composite: 2^6 × 7 = 448.
How do you write 448 in Roman numerals?
448 is CDXLVIII in standard subtractive Roman numeral notation.
What is the binary representation of 448?
448 in decimal is 111000000 in base 2. Adding its active place values gives 256 + 128 + 64 = 448.
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 448
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 448 add to 16. 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.