# 40320

## 40,320 is an even composite number composed of four prime numbers multiplied together.

What does the number 40320 look like?

This visualization shows the relationship between its 4 prime factors (large circles) and 96 divisors.

40320 is an even composite number. It is composed of four distinct prime numbers multiplied together. It has a total of ninety-six divisors.

## Prime factorization of 40320:

### 27 × 32 × 5 × 7

(2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7)

See below for interesting mathematical facts about the number 40320 from the Numbermatics database.

### Names of 40320

• Cardinal: 40320 can be written as Forty thousand, three hundred twenty.

### Scientific notation

• Scientific notation: 4.032 × 104

### Factors of 40320

• Number of distinct prime factors ω(n): 4
• Total number of prime factors Ω(n): 11
• Sum of prime factors: 17

### Divisors of 40320

• Number of divisors d(n): 96
• Complete list of divisors:
• Sum of all divisors σ(n): 159120
• Sum of proper divisors (its aliquot sum) s(n): 118800
• 40320 is an abundant number, because the sum of its proper divisors (118800) is greater than itself. Its abundance is 78480

### Bases of 40320

• Binary: 10011101100000002
• Base-36: V40

### Squares and roots of 40320

• 40320 squared (403202) is 1625702400
• 40320 cubed (403203) is 65548320768000
• The square root of 40320 is 200.7984063681
• The cube root of 40320 is 34.2904755293

### Scales and comparisons

How big is 40320?
• 40,320 seconds is equal to 11 hours, 12 minutes.
• To count from 1 to 40,320 would take you about eleven hours.

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 40320 cubic inches would be around 2.9 feet tall.

### Recreational maths with 40320

• 40320 backwards is 02304
• 40320 is a Harshad number.
• The number of decimal digits it has is: 5
• The sum of 40320's digits is 9
• More coming soon!