Number dictionary · Exact arithmetic
1564: factors and number facts
one thousand five hundred sixty-four 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 sixty-four
- Roman numeral
- MDLXIV
- Prime factorization
- 2^2 × 17 × 23
- Digital root
- 7
All factors of 1564
A positive factor divides 1564 with no remainder. In ascending order, the complete list is:
1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, 1564
Factor pairs
- 1 × 1564 = 1564
- 2 × 782 = 1564
- 4 × 391 = 1564
- 17 × 92 = 1564
- 23 × 68 = 1564
- 34 × 46 = 1564
Each pair describes an arrangement of 1564 items into equal rows. The pairs have different row and column counts; 1564 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 3024
- Sum excluding 1564
- 1460
- Classification
- deficient
1564 is deficient because its proper divisors add to 1460, which is less than 1564.
Prime factorization of 1564
1564 = 2^2 × 17 × 23
Repeated division, step by step
- 1564 ÷ 2 = 782
- 782 ÷ 2 = 391
- 391 ÷ 17 = 23
- 23 ÷ 23 = 1
Multiply the prime divisors in these steps to reconstruct 1564. 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 1559. The next larger prime is 1567. The factor list above explains why 1564 is composite.
Learn the factorization method1564 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand five hundred sixty-four |
| Roman numeral | MDLXIV |
| Binary (base 2) | 11000011100 |
| Octal (base 8) | 3034 |
| Decimal (base 10) | 1564 |
| Hexadecimal (base 16) | 61C |
Check the binary conversion
Read 11000011100 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
1024 + 512 + 16 + 8 + 4 = 1564
Check the hexadecimal conversion
6 × 16^2 + 1 × 16^1 + 12 × 16^0 = 1564
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 1564
- 1564 squared
- 1564 × 1564 = 2,446,096
- 1564 cubed
- 1564 × 1564 × 1564 = 3,825,694,144
- Square root
- ≈ 39.547440
- Simplified radical
- 2√391
1564 lies between 1521 (39²) and 1600 (40²), so it is not a perfect square. It is not a perfect cube.
1564 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1564.
Distinguish a square from a square rootMultiplication table for 1564
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 | 782 | 0 | Yes |
| 3 | 521 | 1 | No |
| 4 | 391 | 0 | Yes |
| 5 | 312 | 4 | No |
| 6 | 260 | 4 | No |
| 7 | 223 | 3 | No |
| 8 | 195 | 4 | No |
| 9 | 173 | 7 | No |
| 10 | 156 | 4 | No |
| 11 | 142 | 2 | No |
| 12 | 130 | 4 | No |
For example, 1564 = 7 × 223 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1564
1564 contains 4 decimal digits. Its digit sum is 1 + 5 + 6 + 4 = 16.
- 1564: 1 + 5 + 6 + 4 = 16
- 16: 1 + 6 = 7
The digital root is 7. Reversing its digits gives 4651; 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, 1564/100 simplifies to 391/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 15.64. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1564 and 12 is 4. Their least common multiple is 4692. The identity GCD × LCM = 1564 × 12 = 18768 checks both results.
Work through GCF and LCMQuestions about 1564
What are the factors of 1564?
The positive factors are 1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, 1564. There are 12 factors, including 1 and 1564.
Is 1564 a prime number?
No. 1564 is composite: 2^2 × 17 × 23 = 1564.
How do you write 1564 in Roman numerals?
1564 is MDLXIV in standard subtractive Roman numeral notation.
What is the binary representation of 1564?
1564 in decimal is 11000011100 in base 2. Adding its active place values gives 1024 + 512 + 16 + 8 + 4 = 1564.
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 1564
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1564 add to 16. 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.