Number dictionary · Exact arithmetic
501: factors and number facts
five hundred one is an odd number and is composite. Its 4 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- five hundred one
- Roman numeral
- DI
- Prime factorization
- 3 × 167
- Digital root
- 6
All factors of 501
A positive factor divides 501 with no remainder. In ascending order, the complete list is:
1, 3, 167, 501
Factor pairs
- 1 × 501 = 501
- 3 × 167 = 501
Each pair describes an arrangement of 501 items into equal rows. The pairs have different row and column counts; 501 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 672
- Sum excluding 501
- 171
- Classification
- deficient
501 is deficient because its proper divisors add to 171, which is less than 501.
Prime factorization of 501
501 = 3 × 167
Repeated division, step by step
- 501 ÷ 3 = 167
- 167 ÷ 167 = 1
Multiply the prime divisors in these steps to reconstruct 501. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 499. The next larger prime is 503. The factor list above explains why 501 is composite.
Learn the factorization method501 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | five hundred one |
| Roman numeral | DI |
| Binary (base 2) | 111110101 |
| Octal (base 8) | 765 |
| Decimal (base 10) | 501 |
| Hexadecimal (base 16) | 1F5 |
Check the binary conversion
Read 111110101 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 + 32 + 16 + 4 + 1 = 501
Check the hexadecimal conversion
1 × 16^2 + 15 × 16^1 + 5 × 16^0 = 501
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 501
- 501 squared
- 501 × 501 = 251,001
- 501 cubed
- 501 × 501 × 501 = 125,751,501
- Square root
- ≈ 22.383029
- Simplified radical
- √501
501 lies between 484 (22²) and 529 (23²), so it is not a perfect square. It is not a perfect cube.
501 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 501.
Distinguish a square from a square rootMultiplication table for 501
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 | 250 | 1 | No |
| 3 | 167 | 0 | Yes |
| 4 | 125 | 1 | No |
| 5 | 100 | 1 | No |
| 6 | 83 | 3 | No |
| 7 | 71 | 4 | No |
| 8 | 62 | 5 | No |
| 9 | 55 | 6 | No |
| 10 | 50 | 1 | No |
| 11 | 45 | 6 | No |
| 12 | 41 | 9 | No |
For example, 501 = 7 × 71 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 501
501 contains 3 decimal digits. Its digit sum is 5 + 0 + 1 = 6.
- 501: 5 + 0 + 1 = 6
The digital root is 6. Reversing its digits gives 105; 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, 501/100 simplifies to 501/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 5.01. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 501 and 12 is 3. Their least common multiple is 2004. The identity GCD × LCM = 501 × 12 = 6012 checks both results.
Work through GCF and LCMQuestions about 501
What are the factors of 501?
The positive factors are 1, 3, 167, 501. There are 4 factors, including 1 and 501.
Is 501 a prime number?
No. 501 is composite: 3 × 167 = 501.
How do you write 501 in Roman numerals?
501 is DI in standard subtractive Roman numeral notation.
What is the binary representation of 501?
501 in decimal is 111110101 in base 2. Adding its active place values gives 256 + 128 + 64 + 32 + 16 + 4 + 1 = 501.
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 501
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 501 add to 6. 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.