Number dictionary · Exact arithmetic
1077: factors and number facts
one thousand seventy-seven 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
- one thousand seventy-seven
- Roman numeral
- MLXXVII
- Prime factorization
- 3 × 359
- Digital root
- 6
All factors of 1077
A positive factor divides 1077 with no remainder. In ascending order, the complete list is:
1, 3, 359, 1077
Factor pairs
- 1 × 1077 = 1077
- 3 × 359 = 1077
Each pair describes an arrangement of 1077 items into equal rows. The pairs have different row and column counts; 1077 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 1440
- Sum excluding 1077
- 363
- Classification
- deficient
1077 is deficient because its proper divisors add to 363, which is less than 1077.
Prime factorization of 1077
1077 = 3 × 359
Repeated division, step by step
- 1077 ÷ 3 = 359
- 359 ÷ 359 = 1
Multiply the prime divisors in these steps to reconstruct 1077. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 1069. The next larger prime is 1087. The factor list above explains why 1077 is composite.
Learn the factorization method1077 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one thousand seventy-seven |
| Roman numeral | MLXXVII |
| Binary (base 2) | 10000110101 |
| Octal (base 8) | 2065 |
| Decimal (base 10) | 1077 |
| Hexadecimal (base 16) | 435 |
Check the binary conversion
Read 10000110101 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
1024 + 32 + 16 + 4 + 1 = 1077
Check the hexadecimal conversion
4 × 16^2 + 3 × 16^1 + 5 × 16^0 = 1077
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 1077
- 1077 squared
- 1077 × 1077 = 1,159,929
- 1077 cubed
- 1077 × 1077 × 1077 = 1,249,243,533
- Square root
- ≈ 32.817678
- Simplified radical
- √1077
1077 lies between 1024 (32²) and 1089 (33²), so it is not a perfect square. It is not a perfect cube.
1077 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 1077.
Distinguish a square from a square rootMultiplication table for 1077
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 | 538 | 1 | No |
| 3 | 359 | 0 | Yes |
| 4 | 269 | 1 | No |
| 5 | 215 | 2 | No |
| 6 | 179 | 3 | No |
| 7 | 153 | 6 | No |
| 8 | 134 | 5 | No |
| 9 | 119 | 6 | No |
| 10 | 107 | 7 | No |
| 11 | 97 | 10 | No |
| 12 | 89 | 9 | No |
For example, 1077 = 7 × 153 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1077
1077 contains 4 decimal digits. Its digit sum is 1 + 0 + 7 + 7 = 15.
- 1077: 1 + 0 + 7 + 7 = 15
- 15: 1 + 5 = 6
The digital root is 6. Reversing its digits gives 7701; 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, 1077/100 simplifies to 1077/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 10.77. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 1077 and 12 is 3. Their least common multiple is 4308. The identity GCD × LCM = 1077 × 12 = 12924 checks both results.
Work through GCF and LCMQuestions about 1077
What are the factors of 1077?
The positive factors are 1, 3, 359, 1077. There are 4 factors, including 1 and 1077.
Is 1077 a prime number?
No. 1077 is composite: 3 × 359 = 1077.
How do you write 1077 in Roman numerals?
1077 is MLXXVII in standard subtractive Roman numeral notation.
What is the binary representation of 1077?
1077 in decimal is 10000110101 in base 2. Adding its active place values gives 1024 + 32 + 16 + 4 + 1 = 1077.
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 1077
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 1077 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.