Number dictionary · Exact arithmetic
7: factors and number facts
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
- seven
- Roman numeral
- VII
- Prime factorization
- 7
- Digital root
- 7
All factors of 7
A positive factor divides 7 with no remainder. In ascending order, the complete list is:
1, 7
Factor pairs
- 1 × 7 = 7
Each pair describes an arrangement of 7 items into equal rows. The pairs have different row and column counts; 7 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 8
- Sum excluding 7
- 1
- Classification
- deficient
7 is deficient because its proper divisors add to 1, which is less than 7.
Prime factorization of 7
7 = 7
Repeated division, step by step
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 7. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 5. The next larger prime is 11. To check 7 for primality, it is sufficient to test possible divisors from 2 through 2.
Learn the factorization method7 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | seven |
| Roman numeral | VII |
| Binary (base 2) | 111 |
| Octal (base 8) | 7 |
| Decimal (base 10) | 7 |
| Hexadecimal (base 16) | 7 |
Check the binary conversion
Read 111 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
4 + 2 + 1 = 7
Check the hexadecimal conversion
7 × 16^0 = 7
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 7
- 7 squared
- 7 × 7 = 49
- 7 cubed
- 7 × 7 × 7 = 343
- Square root
- ≈ 2.645751
- Simplified radical
- √7
7 lies between 4 (2²) and 9 (3²), so it is not a perfect square. It is not a perfect cube.
7 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 7.
Distinguish a square from a square rootMultiplication table for 7
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 | 3 | 1 | No |
| 3 | 2 | 1 | No |
| 4 | 1 | 3 | No |
| 5 | 1 | 2 | No |
| 6 | 1 | 1 | No |
| 7 | 1 | 0 | Yes |
| 8 | 0 | 7 | No |
| 9 | 0 | 7 | No |
| 10 | 0 | 7 | No |
| 11 | 0 | 7 | No |
| 12 | 0 | 7 | No |
For example, 7 = 7 × 1 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 7
7 contains 1 decimal digit. Its digit sum is 7 = 7.
It already has one digit, so there is no reduction step.
The digital root is 7. 7 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, 7/100 simplifies to 7/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 0.07.
The greatest common divisor of 7 and 12 is 1. Their least common multiple is 84. The identity GCD × LCM = 7 × 12 = 84 checks both results.
Work through GCF and LCMQuestions about 7
What are the factors of 7?
The positive factors are 1, 7. There are 2 factors, including 1 and 7.
Is 7 a prime number?
Yes. The only positive divisors of 7 are 1 and 7.
How do you write 7 in Roman numerals?
7 is VII in standard subtractive Roman numeral notation.
What is the binary representation of 7?
7 in decimal is 111 in base 2. Adding its active place values gives 4 + 2 + 1 = 7.
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.