Number dictionary · Exact arithmetic
737: factors and number facts
seven hundred thirty-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
- seven hundred thirty-seven
- Roman numeral
- DCCXXXVII
- Prime factorization
- 11 × 67
- Digital root
- 8
All factors of 737
A positive factor divides 737 with no remainder. In ascending order, the complete list is:
1, 11, 67, 737
Factor pairs
- 1 × 737 = 737
- 11 × 67 = 737
Each pair describes an arrangement of 737 items into equal rows. The pairs have different row and column counts; 737 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 816
- Sum excluding 737
- 79
- Classification
- deficient
737 is deficient because its proper divisors add to 79, which is less than 737.
Prime factorization of 737
737 = 11 × 67
Repeated division, step by step
- 737 ÷ 11 = 67
- 67 ÷ 67 = 1
Multiply the prime divisors in these steps to reconstruct 737. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 733. The next larger prime is 739. The factor list above explains why 737 is composite.
Learn the factorization method737 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven hundred thirty-seven |
| Roman numeral | DCCXXXVII |
| Binary (base 2) | 1011100001 |
| Octal (base 8) | 1341 |
| Decimal (base 10) | 737 |
| Hexadecimal (base 16) | 2E1 |
Check the binary conversion
Read 1011100001 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 128 + 64 + 32 + 1 = 737
Check the hexadecimal conversion
2 × 16^2 + 14 × 16^1 + 1 × 16^0 = 737
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 737
- 737 squared
- 737 × 737 = 543,169
- 737 cubed
- 737 × 737 × 737 = 400,315,553
- Square root
- ≈ 27.147744
- Simplified radical
- √737
737 lies between 729 (27²) and 784 (28²), so it is not a perfect square. It is not a perfect cube.
737 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 737.
Distinguish a square from a square rootMultiplication table for 737
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 | 368 | 1 | No |
| 3 | 245 | 2 | No |
| 4 | 184 | 1 | No |
| 5 | 147 | 2 | No |
| 6 | 122 | 5 | No |
| 7 | 105 | 2 | No |
| 8 | 92 | 1 | No |
| 9 | 81 | 8 | No |
| 10 | 73 | 7 | No |
| 11 | 67 | 0 | Yes |
| 12 | 61 | 5 | No |
For example, 737 = 7 × 105 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 737
737 contains 3 decimal digits. Its digit sum is 7 + 3 + 7 = 17.
- 737: 7 + 3 + 7 = 17
- 17: 1 + 7 = 8
The digital root is 8. 737 reads the same forward and backward, making it 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, 737/100 simplifies to 737/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 7.37. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 737 and 12 is 1. Their least common multiple is 8844. The identity GCD × LCM = 737 × 12 = 8844 checks both results.
Work through GCF and LCMQuestions about 737
What are the factors of 737?
The positive factors are 1, 11, 67, 737. There are 4 factors, including 1 and 737.
Is 737 a prime number?
No. 737 is composite: 11 × 67 = 737.
How do you write 737 in Roman numerals?
737 is DCCXXXVII in standard subtractive Roman numeral notation.
What is the binary representation of 737?
737 in decimal is 1011100001 in base 2. Adding its active place values gives 512 + 128 + 64 + 32 + 1 = 737.
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 737
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 737 add to 17. 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.