Number dictionary · Exact arithmetic
401: factors and number facts
four hundred one is an odd number and is prime. Its 2 positive divisors form 1 factor pair.
Number JD Editorial Team · Updated 2026-10-08
- In words
- four hundred one
- Roman numeral
- CDI
- Prime factorization
- 401
- Digital root
- 5
All factors of 401
A positive factor divides 401 with no remainder. In ascending order, the complete list is:
1, 401
Factor pairs
- 1 × 401 = 401
Each pair describes an arrangement of 401 items into equal rows. The pairs have different row and column counts; 401 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 402
- Sum excluding 401
- 1
- Classification
- deficient
401 is deficient because its proper divisors add to 1, which is less than 401.
Prime factorization of 401
401 = 401
Repeated division, step by step
- 401 ÷ 401 = 1
Multiply the prime divisors in these steps to reconstruct 401. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 397. The next larger prime is 409. To check 401 for primality, it is sufficient to test possible divisors from 2 through 20.
Learn the factorization method401 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred one |
| Roman numeral | CDI |
| Binary (base 2) | 110010001 |
| Octal (base 8) | 621 |
| Decimal (base 10) | 401 |
| Hexadecimal (base 16) | 191 |
Check the binary conversion
Read 110010001 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 + 16 + 1 = 401
Check the hexadecimal conversion
1 × 16^2 + 9 × 16^1 + 1 × 16^0 = 401
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 401
- 401 squared
- 401 × 401 = 160,801
- 401 cubed
- 401 × 401 × 401 = 64,481,201
- Square root
- ≈ 20.024984
- Simplified radical
- √401
401 lies between 400 (20²) and 441 (21²), so it is not a perfect square. It is not a perfect cube.
401 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 401.
Distinguish a square from a square rootMultiplication table for 401
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 | 200 | 1 | No |
| 3 | 133 | 2 | No |
| 4 | 100 | 1 | No |
| 5 | 80 | 1 | No |
| 6 | 66 | 5 | No |
| 7 | 57 | 2 | No |
| 8 | 50 | 1 | No |
| 9 | 44 | 5 | No |
| 10 | 40 | 1 | No |
| 11 | 36 | 5 | No |
| 12 | 33 | 5 | No |
For example, 401 = 7 × 57 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 401
401 contains 3 decimal digits. Its digit sum is 4 + 0 + 1 = 5.
- 401: 4 + 0 + 1 = 5
The digital root is 5. Reversing its digits gives 104; 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, 401/100 simplifies to 401/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 4.01. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 401 and 12 is 1. Their least common multiple is 4812. The identity GCD × LCM = 401 × 12 = 4812 checks both results.
Work through GCF and LCMQuestions about 401
What are the factors of 401?
The positive factors are 1, 401. There are 2 factors, including 1 and 401.
Is 401 a prime number?
Yes. The only positive divisors of 401 are 1 and 401.
How do you write 401 in Roman numerals?
401 is CDI in standard subtractive Roman numeral notation.
What is the binary representation of 401?
401 in decimal is 110010001 in base 2. Adding its active place values gives 256 + 128 + 16 + 1 = 401.
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 401
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 401 add to 5. 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.