Number dictionary · Exact arithmetic
1508: factors and number facts
one thousand five hundred eight is an even number and is composite. Its 12 positive divisors form 6 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one thousand five hundred eight
- Roman numeral
- MDVIII
- Prime factorization
- 2^2 × 13 × 29
- Digital root
- 5
All factors of 1508
A positive factor divides 1508 with no remainder. In ascending order, the complete list is:
1, 2, 4, 13, 26, 29, 52, 58, 116, 377, 754, 1508
Factor pairs
- 1 × 1508 = 1508
- 2 × 754 = 1508
- 4 × 377 = 1508
- 13 × 116 = 1508
- 26 × 58 = 1508
- 29 × 52 = 1508
Each pair describes an arrangement of 1508 items into equal rows. The pairs have different row and column counts; 1508 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 2940
- Sum excluding 1508
- 1432
- Classification
- deficient
1508 is deficient because its proper divisors add to 1432, which is less than 1508.
Prime factorization of 1508
1508 = 2^2 × 13 × 29
Repeated division, step by step
- 1508 ÷ 2 = 754
- 754 ÷ 2 = 377
- 377 ÷ 13 = 29
- 29 ÷ 29 = 1
Multiply the prime divisors in these steps to reconstruct 1508. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) × (1 + 1) = 12.
The preceding prime is 1499. The next larger prime is 1511. The factor list above explains why 1508 is composite.
Learn the factorization method1508 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand five hundred eight |
| Roman numeral | MDVIII |
| Binary (base 2) | 10111100100 |
| Octal (base 8) | 2744 |
| Decimal (base 10) | 1508 |
| Hexadecimal (base 16) | 5E4 |
Check the binary conversion
Read 10111100100 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
1024 + 256 + 128 + 64 + 32 + 4 = 1508
Check the hexadecimal conversion
5 × 16^2 + 14 × 16^1 + 4 × 16^0 = 1508
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 1508
- 1508 squared
- 1508 × 1508 = 2,274,064
- 1508 cubed
- 1508 × 1508 × 1508 = 3,429,288,512
- Square root
- ≈ 38.832976
- Simplified radical
- 2√377
1508 lies between 1444 (38²) and 1521 (39²), so it is not a perfect square. It is not a perfect cube.
1508 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1508.
Distinguish a square from a square rootMultiplication table for 1508
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 | 754 | 0 | Yes |
| 3 | 502 | 2 | No |
| 4 | 377 | 0 | Yes |
| 5 | 301 | 3 | No |
| 6 | 251 | 2 | No |
| 7 | 215 | 3 | No |
| 8 | 188 | 4 | No |
| 9 | 167 | 5 | No |
| 10 | 150 | 8 | No |
| 11 | 137 | 1 | No |
| 12 | 125 | 8 | No |
For example, 1508 = 7 × 215 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1508
1508 contains 4 decimal digits. Its digit sum is 1 + 5 + 0 + 8 = 14.
- 1508: 1 + 5 + 0 + 8 = 14
- 14: 1 + 4 = 5
The digital root is 5. Reversing its digits gives 8051; 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, 1508/100 simplifies to 377/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 15.08. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1508 and 12 is 4. Their least common multiple is 4524. The identity GCD × LCM = 1508 × 12 = 18096 checks both results.
Work through GCF and LCMQuestions about 1508
What are the factors of 1508?
The positive factors are 1, 2, 4, 13, 26, 29, 52, 58, 116, 377, 754, 1508. There are 12 factors, including 1 and 1508.
Is 1508 a prime number?
No. 1508 is composite: 2^2 × 13 × 29 = 1508.
How do you write 1508 in Roman numerals?
1508 is MDVIII in standard subtractive Roman numeral notation.
What is the binary representation of 1508?
1508 in decimal is 10111100100 in base 2. Adding its active place values gives 1024 + 256 + 128 + 64 + 32 + 4 = 1508.
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 1508
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1508 add to 14. 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.