Number dictionary · Exact arithmetic
137: factors and number facts
one hundred thirty-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
- one hundred thirty-seven
- Roman numeral
- CXXXVII
- Prime factorization
- 137
- Digital root
- 2
All factors of 137
A positive factor divides 137 with no remainder. In ascending order, the complete list is:
1, 137
Factor pairs
- 1 × 137 = 137
Each pair describes an arrangement of 137 items into equal rows. The pairs have different row and column counts; 137 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 138
- Sum excluding 137
- 1
- Classification
- deficient
137 is deficient because its proper divisors add to 1, which is less than 137.
Prime factorization of 137
137 = 137
Repeated division, step by step
- 137 ÷ 137 = 1
Multiply the prime divisors in these steps to reconstruct 137. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 131. The next larger prime is 139. To check 137 for primality, it is sufficient to test possible divisors from 2 through 11.
Learn the factorization method137 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one hundred thirty-seven |
| Roman numeral | CXXXVII |
| Binary (base 2) | 10001001 |
| Octal (base 8) | 211 |
| Decimal (base 10) | 137 |
| Hexadecimal (base 16) | 89 |
Check the binary conversion
Read 10001001 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
128 + 8 + 1 = 137
Check the hexadecimal conversion
8 × 16^1 + 9 × 16^0 = 137
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 137
- 137 squared
- 137 × 137 = 18,769
- 137 cubed
- 137 × 137 × 137 = 2,571,353
- Square root
- ≈ 11.704700
- Simplified radical
- √137
137 lies between 121 (11²) and 144 (12²), so it is not a perfect square. It is not a perfect cube.
137 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 137.
Distinguish a square from a square rootMultiplication table for 137
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 | 68 | 1 | No |
| 3 | 45 | 2 | No |
| 4 | 34 | 1 | No |
| 5 | 27 | 2 | No |
| 6 | 22 | 5 | No |
| 7 | 19 | 4 | No |
| 8 | 17 | 1 | No |
| 9 | 15 | 2 | No |
| 10 | 13 | 7 | No |
| 11 | 12 | 5 | No |
| 12 | 11 | 5 | No |
For example, 137 = 7 × 19 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 137
137 contains 3 decimal digits. Its digit sum is 1 + 3 + 7 = 11.
- 137: 1 + 3 + 7 = 11
- 11: 1 + 1 = 2
The digital root is 2. Reversing its digits gives 731; 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, 137/100 simplifies to 137/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 1.37. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 137 and 12 is 1. Their least common multiple is 1644. The identity GCD × LCM = 137 × 12 = 1644 checks both results.
Work through GCF and LCMQuestions about 137
What are the factors of 137?
The positive factors are 1, 137. There are 2 factors, including 1 and 137.
Is 137 a prime number?
Yes. The only positive divisors of 137 are 1 and 137.
How do you write 137 in Roman numerals?
137 is CXXXVII in standard subtractive Roman numeral notation.
What is the binary representation of 137?
137 in decimal is 10001001 in base 2. Adding its active place values gives 128 + 8 + 1 = 137.
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 137
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 137 add to 11. 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.