Number dictionary · Exact arithmetic
977: factors and number facts
nine hundred seventy-seven is an odd number and is prime. Its 2 positive divisors form 1 factor pair.
Number JD Editorial Team · Updated 2026-10-08
- In words
- nine hundred seventy-seven
- Roman numeral
- CMLXXVII
- Prime factorization
- 977
- Digital root
- 5
All factors of 977
A positive factor divides 977 with no remainder. In ascending order, the complete list is:
1, 977
Factor pairs
- 1 × 977 = 977
Each pair describes an arrangement of 977 items into equal rows. The pairs have different row and column counts; 977 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 978
- Sum excluding 977
- 1
- Classification
- deficient
977 is deficient because its proper divisors add to 1, which is less than 977.
Prime factorization of 977
977 = 977
Repeated division, step by step
- 977 ÷ 977 = 1
Multiply the prime divisors in these steps to reconstruct 977. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 971. The next larger prime is 983. To check 977 for primality, it is sufficient to test possible divisors from 2 through 31.
Learn the factorization method977 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | nine hundred seventy-seven |
| Roman numeral | CMLXXVII |
| Binary (base 2) | 1111010001 |
| Octal (base 8) | 1721 |
| Decimal (base 10) | 977 |
| Hexadecimal (base 16) | 3D1 |
Check the binary conversion
Read 1111010001 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 256 + 128 + 64 + 16 + 1 = 977
Check the hexadecimal conversion
3 × 16^2 + 13 × 16^1 + 1 × 16^0 = 977
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 977
- 977 squared
- 977 × 977 = 954,529
- 977 cubed
- 977 × 977 × 977 = 932,574,833
- Square root
- ≈ 31.256999
- Simplified radical
- √977
977 lies between 961 (31²) and 1024 (32²), so it is not a perfect square. It is not a perfect cube.
977 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 977.
Distinguish a square from a square rootMultiplication table for 977
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 | 488 | 1 | No |
| 3 | 325 | 2 | No |
| 4 | 244 | 1 | No |
| 5 | 195 | 2 | No |
| 6 | 162 | 5 | No |
| 7 | 139 | 4 | No |
| 8 | 122 | 1 | No |
| 9 | 108 | 5 | No |
| 10 | 97 | 7 | No |
| 11 | 88 | 9 | No |
| 12 | 81 | 5 | No |
For example, 977 = 7 × 139 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 977
977 contains 3 decimal digits. Its digit sum is 9 + 7 + 7 = 23.
- 977: 9 + 7 + 7 = 23
- 23: 2 + 3 = 5
The digital root is 5. Reversing its digits gives 779; 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, 977/100 simplifies to 977/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 9.77. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 977 and 12 is 1. Their least common multiple is 11724. The identity GCD × LCM = 977 × 12 = 11724 checks both results.
Work through GCF and LCMQuestions about 977
What are the factors of 977?
The positive factors are 1, 977. There are 2 factors, including 1 and 977.
Is 977 a prime number?
Yes. The only positive divisors of 977 are 1 and 977.
How do you write 977 in Roman numerals?
977 is CMLXXVII in standard subtractive Roman numeral notation.
What is the binary representation of 977?
977 in decimal is 1111010001 in base 2. Adding its active place values gives 512 + 256 + 128 + 64 + 16 + 1 = 977.
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 977
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 977 add to 23. 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.