# 2048

## 2,048 is an even composite number. It is composed of a single prime number multiplied by itself ten times.

What does the number 2048 look like?

This visualization shows the relationship between its 1 prime factors (large circles) and 12 divisors.

2048 is an even composite number. It is composed of one distinct prime number multiplied by itself ten times. It has a total of twelve divisors.

## Prime factorization of 2048:

### 211

(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2)

See below for interesting mathematical facts about the number 2048 from the Numbermatics database.

### Names of 2048

• Cardinal: 2048 can be written as Two thousand and forty-eight.

### Scientific notation

• Scientific notation: 2.048 × 103

### Factors of 2048

• Number of distinct prime factors ω(n): 1
• Total number of prime factors Ω(n): 11
• Sum of prime factors: 2

### Divisors of 2048

• Number of divisors d(n): 12
• Complete list of divisors:
• Sum of all divisors σ(n): 4095
• Sum of proper divisors (its aliquot sum) s(n): 2047
• 2048 is a deficient number, because the sum of its proper divisors (2047) is less than itself. Its deficiency is 1

### Bases of 2048

• Binary: 1000000000002
• Base-36: 1KW

### Squares and roots of 2048

• 2048 squared (20482) is 4194304
• 2048 cubed (20483) is 8589934592
• The square root of 2048 is 45.2548339959
• The cube root of 2048 is 12.6992084155

### Scales and comparisons

How big is 2048?
• 2,048 seconds is equal to 34 minutes, 8 seconds.
• To count from 1 to 2,048 would take you about thirty-four minutes.

This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)

• A cube with a volume of 2048 cubic inches would be around 1.1 feet tall.

### Recreational maths with 2048

• 2048 backwards is 8402
• The number of decimal digits it has is: 4
• The sum of 2048's digits is 14
• More coming soon!