Number dictionary · Exact arithmetic
1264: factors and number facts
one thousand two hundred sixty-four is an even number and is composite. Its 10 positive divisors form 5 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one thousand two hundred sixty-four
- Roman numeral
- MCCLXIV
- Prime factorization
- 2^4 × 79
- Digital root
- 4
All factors of 1264
A positive factor divides 1264 with no remainder. In ascending order, the complete list is:
1, 2, 4, 8, 16, 79, 158, 316, 632, 1264
Factor pairs
- 1 × 1264 = 1264
- 2 × 632 = 1264
- 4 × 316 = 1264
- 8 × 158 = 1264
- 16 × 79 = 1264
Each pair describes an arrangement of 1264 items into equal rows. The pairs have different row and column counts; 1264 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 10
- Sum of all divisors
- 2480
- Sum excluding 1264
- 1216
- Classification
- deficient
1264 is deficient because its proper divisors add to 1216, which is less than 1264.
Prime factorization of 1264
1264 = 2^4 × 79
Repeated division, step by step
- 1264 ÷ 2 = 632
- 632 ÷ 2 = 316
- 316 ÷ 2 = 158
- 158 ÷ 2 = 79
- 79 ÷ 79 = 1
Multiply the prime divisors in these steps to reconstruct 1264. An exponent records how many times the same prime occurs. The divisor-count calculation is (4 + 1) × (1 + 1) = 10.
The preceding prime is 1259. The next larger prime is 1277. The factor list above explains why 1264 is composite.
Learn the factorization method1264 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand two hundred sixty-four |
| Roman numeral | MCCLXIV |
| Binary (base 2) | 10011110000 |
| Octal (base 8) | 2360 |
| Decimal (base 10) | 1264 |
| Hexadecimal (base 16) | 4F0 |
Check the binary conversion
Read 10011110000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
1024 + 128 + 64 + 32 + 16 = 1264
Check the hexadecimal conversion
4 × 16^2 + 15 × 16^1 + 0 × 16^0 = 1264
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 1264
- 1264 squared
- 1264 × 1264 = 1,597,696
- 1264 cubed
- 1264 × 1264 × 1264 = 2,019,487,744
- Square root
- ≈ 35.552778
- Simplified radical
- 4√79
1264 lies between 1225 (35²) and 1296 (36²), so it is not a perfect square. It is not a perfect cube.
1264 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1264.
Distinguish a square from a square rootMultiplication table for 1264
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 | 632 | 0 | Yes |
| 3 | 421 | 1 | No |
| 4 | 316 | 0 | Yes |
| 5 | 252 | 4 | No |
| 6 | 210 | 4 | No |
| 7 | 180 | 4 | No |
| 8 | 158 | 0 | Yes |
| 9 | 140 | 4 | No |
| 10 | 126 | 4 | No |
| 11 | 114 | 10 | No |
| 12 | 105 | 4 | No |
For example, 1264 = 7 × 180 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1264
1264 contains 4 decimal digits. Its digit sum is 1 + 2 + 6 + 4 = 13.
- 1264: 1 + 2 + 6 + 4 = 13
- 13: 1 + 3 = 4
The digital root is 4. Reversing its digits gives 4621; 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, 1264/100 simplifies to 316/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 12.64. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1264 and 12 is 4. Their least common multiple is 3792. The identity GCD × LCM = 1264 × 12 = 15168 checks both results.
Work through GCF and LCMQuestions about 1264
What are the factors of 1264?
The positive factors are 1, 2, 4, 8, 16, 79, 158, 316, 632, 1264. There are 10 factors, including 1 and 1264.
Is 1264 a prime number?
No. 1264 is composite: 2^4 × 79 = 1264.
How do you write 1264 in Roman numerals?
1264 is MCCLXIV in standard subtractive Roman numeral notation.
What is the binary representation of 1264?
1264 in decimal is 10011110000 in base 2. Adding its active place values gives 1024 + 128 + 64 + 32 + 16 = 1264.
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 1264
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1264 add to 13. 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.