Number dictionary · Exact arithmetic
49: factors and number facts
forty-nine is an odd number and is composite. Its 3 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- forty-nine
- Roman numeral
- XLIX
- Prime factorization
- 7^2
- Digital root
- 4
All factors of 49
A positive factor divides 49 with no remainder. In ascending order, the complete list is:
1, 7, 49
Factor pairs
- 1 × 49 = 49
- 7 × 7 = 49
Each pair describes an arrangement of 49 items into equal rows. The 7 × 7 pair is square, so its shared factor appears only once in the factor list.
Divisor totals
- Positive divisors
- 3
- Sum of all divisors
- 57
- Sum excluding 49
- 8
- Classification
- deficient
49 is deficient because its proper divisors add to 8, which is less than 49.
Prime factorization of 49
49 = 7^2
Repeated division, step by step
- 49 ÷ 7 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 49. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) = 3.
The preceding prime is 47. The next larger prime is 53. The factor list above explains why 49 is composite.
Learn the factorization method49 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | forty-nine |
| Roman numeral | XLIX |
| Binary (base 2) | 110001 |
| Octal (base 8) | 61 |
| Decimal (base 10) | 49 |
| Hexadecimal (base 16) | 31 |
Check the binary conversion
Read 110001 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
32 + 16 + 1 = 49
Check the hexadecimal conversion
3 × 16^1 + 1 × 16^0 = 49
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 49
- 49 squared
- 49 × 49 = 2,401
- 49 cubed
- 49 × 49 × 49 = 117,649
- Square root
- = 7
- Simplified radical
- 7
49 is a perfect square: 7 × 7 = 49. It is not a perfect cube.
49 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 49.
Distinguish a square from a square rootMultiplication table for 49
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 | 24 | 1 | No |
| 3 | 16 | 1 | No |
| 4 | 12 | 1 | No |
| 5 | 9 | 4 | No |
| 6 | 8 | 1 | No |
| 7 | 7 | 0 | Yes |
| 8 | 6 | 1 | No |
| 9 | 5 | 4 | No |
| 10 | 4 | 9 | No |
| 11 | 4 | 5 | No |
| 12 | 4 | 1 | No |
For example, 49 = 7 × 7 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 49
49 contains 2 decimal digits. Its digit sum is 4 + 9 = 13.
- 49: 4 + 9 = 13
- 13: 1 + 3 = 4
The digital root is 4. Reversing its digits gives 94; 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, 49/100 simplifies to 49/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 0.49.
The greatest common divisor of 49 and 12 is 1. Their least common multiple is 588. The identity GCD × LCM = 49 × 12 = 588 checks both results.
Work through GCF and LCMQuestions about 49
What are the factors of 49?
The positive factors are 1, 7, 49. There are 3 factors, including 1 and 49.
Is 49 a prime number?
No. 49 is composite: 7^2 = 49.
How do you write 49 in Roman numerals?
49 is XLIX in standard subtractive Roman numeral notation.
What is the binary representation of 49?
49 in decimal is 110001 in base 2. Adding its active place values gives 32 + 16 + 1 = 49.
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 49
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 49 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.