Number dictionary · Exact arithmetic
442: factors and number facts
four hundred forty-two 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 forty-two
- Roman numeral
- CDXLII
- Prime factorization
- 2 × 13 × 17
- Digital root
- 1
All factors of 442
A positive factor divides 442 with no remainder. In ascending order, the complete list is:
1, 2, 13, 17, 26, 34, 221, 442
Factor pairs
- 1 × 442 = 442
- 2 × 221 = 442
- 13 × 34 = 442
- 17 × 26 = 442
Each pair describes an arrangement of 442 items into equal rows. The pairs have different row and column counts; 442 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 756
- Sum excluding 442
- 314
- Classification
- deficient
442 is deficient because its proper divisors add to 314, which is less than 442.
Prime factorization of 442
442 = 2 × 13 × 17
Repeated division, step by step
- 442 ÷ 2 = 221
- 221 ÷ 13 = 17
- 17 ÷ 17 = 1
Multiply the prime divisors in these steps to reconstruct 442. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) × (1 + 1) = 8.
The preceding prime is 439. The next larger prime is 443. The factor list above explains why 442 is composite.
Learn the factorization method442 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred forty-two |
| Roman numeral | CDXLII |
| Binary (base 2) | 110111010 |
| Octal (base 8) | 672 |
| Decimal (base 10) | 442 |
| Hexadecimal (base 16) | 1BA |
Check the binary conversion
Read 110111010 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 + 32 + 16 + 8 + 2 = 442
Check the hexadecimal conversion
1 × 16^2 + 11 × 16^1 + 10 × 16^0 = 442
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 442
- 442 squared
- 442 × 442 = 195,364
- 442 cubed
- 442 × 442 × 442 = 86,350,888
- Square root
- ≈ 21.023796
- Simplified radical
- √442
442 lies between 441 (21²) and 484 (22²), so it is not a perfect square. It is not a perfect cube.
442 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 442.
Distinguish a square from a square rootMultiplication table for 442
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 | 221 | 0 | Yes |
| 3 | 147 | 1 | No |
| 4 | 110 | 2 | No |
| 5 | 88 | 2 | No |
| 6 | 73 | 4 | No |
| 7 | 63 | 1 | No |
| 8 | 55 | 2 | No |
| 9 | 49 | 1 | No |
| 10 | 44 | 2 | No |
| 11 | 40 | 2 | No |
| 12 | 36 | 10 | No |
For example, 442 = 7 × 63 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 442
442 contains 3 decimal digits. Its digit sum is 4 + 4 + 2 = 10.
- 442: 4 + 4 + 2 = 10
- 10: 1 + 0 = 1
The digital root is 1. Reversing its digits gives 244; 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, 442/100 simplifies to 221/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 4.42. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 442 and 12 is 2. Their least common multiple is 2652. The identity GCD × LCM = 442 × 12 = 5304 checks both results.
Work through GCF and LCMQuestions about 442
What are the factors of 442?
The positive factors are 1, 2, 13, 17, 26, 34, 221, 442. There are 8 factors, including 1 and 442.
Is 442 a prime number?
No. 442 is composite: 2 × 13 × 17 = 442.
How do you write 442 in Roman numerals?
442 is CDXLII in standard subtractive Roman numeral notation.
What is the binary representation of 442?
442 in decimal is 110111010 in base 2. Adding its active place values gives 256 + 128 + 32 + 16 + 8 + 2 = 442.
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 442
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 442 add to 10. 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.