Number dictionary · Exact arithmetic
1: factors and number facts
one is an odd number and is neither prime nor composite. It is the multiplicative identity: multiplying any number by 1 leaves that number unchanged.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one
- Roman numeral
- I
- Prime factorization
- No prime factors
- Digital root
- 1
All factors of 1
A positive factor divides 1 with no remainder. In ascending order, the complete list is:
1
Factor pairs
- 1 × 1 = 1
Each pair describes an arrangement of 1 items into equal rows. The 1 × 1 pair is square, so its shared factor appears only once in the factor list.
Divisor totals
- Positive divisors
- 1
- Sum of all divisors
- 1
- Sum excluding 1
- 0
- Classification
- deficient
1 is deficient because its proper divisors add to 0, which is less than 1. The sum of an empty set of proper positive divisors is 0.
Prime factorization of 1
One has no prime factors. It is neither prime nor composite, and it is not included as a prime factor in the factorization of a larger integer.
There is no smaller positive prime. The next larger prime is 2. The factor list above explains why 1 is neither prime nor composite.
Learn the factorization method1 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one |
| Roman numeral | I |
| Binary (base 2) | 1 |
| Octal (base 8) | 1 |
| Decimal (base 10) | 1 |
| Hexadecimal (base 16) | 1 |
Check the binary conversion
Read 1 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
1 = 1
Check the hexadecimal conversion
1 × 16^0 = 1
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 1
- 1 squared
- 1 × 1 = 1
- 1 cubed
- 1 × 1 × 1 = 1
- Square root
- = 1
- Simplified radical
- 1
1 is a perfect square: 1 × 1 = 1. It is also a perfect cube: 1³ = 1.
1 is triangular: it is the sum of the integers from 1 through 1.
Distinguish a square from a square rootMultiplication table for 1
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 | 0 | 1 | No |
| 3 | 0 | 1 | No |
| 4 | 0 | 1 | No |
| 5 | 0 | 1 | No |
| 6 | 0 | 1 | No |
| 7 | 0 | 1 | No |
| 8 | 0 | 1 | No |
| 9 | 0 | 1 | No |
| 10 | 0 | 1 | No |
| 11 | 0 | 1 | No |
| 12 | 0 | 1 | No |
For example, 1 = 7 × 0 + 1. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 1
1 contains 1 decimal digit. Its digit sum is 1 = 1.
It already has one digit, so there is no reduction step.
The digital root is 1. 1 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, 1/100 simplifies to 1/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 0.01.
The greatest common divisor of 1 and 12 is 1. Their least common multiple is 12. The identity GCD × LCM = 1 × 12 = 12 checks both results.
Work through GCF and LCMQuestions about 1
What are the factors of 1?
The positive factors are 1. There is 1 factor, including 1 and no other positive divisor.
Is 1 a prime number?
No. One has only one positive divisor. A prime must have exactly two distinct positive divisors.
How do you write 1 in Roman numerals?
1 is I in standard subtractive Roman numeral notation.
What is the binary representation of 1?
1 in decimal is 1 in base 2. Adding its active place values gives 1 = 1.
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.