Number dictionary · Exact arithmetic
1464: factors and number facts
one thousand four hundred sixty-four is an even number and is composite. Its 16 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one thousand four hundred sixty-four
- Roman numeral
- MCDLXIV
- Prime factorization
- 2^3 × 3 × 61
- Digital root
- 6
All factors of 1464
A positive factor divides 1464 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, 1464
Factor pairs
- 1 × 1464 = 1464
- 2 × 732 = 1464
- 3 × 488 = 1464
- 4 × 366 = 1464
- 6 × 244 = 1464
- 8 × 183 = 1464
- 12 × 122 = 1464
- 24 × 61 = 1464
Each pair describes an arrangement of 1464 items into equal rows. The pairs have different row and column counts; 1464 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 3720
- Sum excluding 1464
- 2256
- Classification
- abundant
1464 is abundant because its proper divisors add to 2256, which is greater than 1464.
Prime factorization of 1464
1464 = 2^3 × 3 × 61
Repeated division, step by step
- 1464 ÷ 2 = 732
- 732 ÷ 2 = 366
- 366 ÷ 2 = 183
- 183 ÷ 3 = 61
- 61 ÷ 61 = 1
Multiply the prime divisors in these steps to reconstruct 1464. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) × (1 + 1) = 16.
The preceding prime is 1459. The next larger prime is 1471. The factor list above explains why 1464 is composite.
Learn the factorization method1464 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand four hundred sixty-four |
| Roman numeral | MCDLXIV |
| Binary (base 2) | 10110111000 |
| Octal (base 8) | 2670 |
| Decimal (base 10) | 1464 |
| Hexadecimal (base 16) | 5B8 |
Check the binary conversion
Read 10110111000 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 + 32 + 16 + 8 = 1464
Check the hexadecimal conversion
5 × 16^2 + 11 × 16^1 + 8 × 16^0 = 1464
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 1464
- 1464 squared
- 1464 × 1464 = 2,143,296
- 1464 cubed
- 1464 × 1464 × 1464 = 3,137,785,344
- Square root
- ≈ 38.262253
- Simplified radical
- 2√366
1464 lies between 1444 (38²) and 1521 (39²), so it is not a perfect square. It is not a perfect cube.
1464 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1464.
Distinguish a square from a square rootMultiplication table for 1464
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 | 732 | 0 | Yes |
| 3 | 488 | 0 | Yes |
| 4 | 366 | 0 | Yes |
| 5 | 292 | 4 | No |
| 6 | 244 | 0 | Yes |
| 7 | 209 | 1 | No |
| 8 | 183 | 0 | Yes |
| 9 | 162 | 6 | No |
| 10 | 146 | 4 | No |
| 11 | 133 | 1 | No |
| 12 | 122 | 0 | Yes |
For example, 1464 = 7 × 209 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1464
1464 contains 4 decimal digits. Its digit sum is 1 + 4 + 6 + 4 = 15.
- 1464: 1 + 4 + 6 + 4 = 15
- 15: 1 + 5 = 6
The digital root is 6. Reversing its digits gives 4641; 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, 1464/100 simplifies to 366/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 14.64. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1464 and 12 is 12. Their least common multiple is 1464. The identity GCD × LCM = 1464 × 12 = 17568 checks both results.
Work through GCF and LCMQuestions about 1464
What are the factors of 1464?
The positive factors are 1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, 1464. There are 16 factors, including 1 and 1464.
Is 1464 a prime number?
No. 1464 is composite: 2^3 × 3 × 61 = 1464.
How do you write 1464 in Roman numerals?
1464 is MCDLXIV in standard subtractive Roman numeral notation.
What is the binary representation of 1464?
1464 in decimal is 10110111000 in base 2. Adding its active place values gives 1024 + 256 + 128 + 32 + 16 + 8 = 1464.
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 1464
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1464 add to 15. 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.