72

Notation

72 can be expressed in many ways apart from the usual decimal (base-10) notation. It can be written out in wordswith formatting and even extra punctuation added depending on the language. In more technical situationsnumbers are commmonly expressed in scientific notation or in different base systems such as binary or hex.

• Written form in US english: ‘Seventy-two’
• Written form in British english: ‘Seventy-two’
• Scientific notation: 7.2 × 10¹
• Binary (base-2): 1001000₂
• Octal (base-8): 110₈
• Hexadecimal (base-16): 0x48
• Base-36: 20

Prime factorization of 72

Prime factors are the prime numbers that multiply together to form that number. You could say that a number is made or ‘composed’ of its prime factors. Every whole number greater than one is formed from at least one prime factor. (Prime numbers have only one prime factor: themselves.)

Calculating the prime factors of a number is known as prime factorization. For very large numbers this can be a challenging task.

How many prime factors does 72 have?

It has two distinct prime factors.

• Number of distinct prime factors ω(n): 2
• Total number of prime factors including multiple instances Ω(n): 5
• Prime factorization: 2^3 × 3^2
• Here is a list of the distinct prime factors:
  2 3
• Sum of distinct prime factors: 5
• Sum of all prime factors (sum with multiplicity): 12

Divisors of 72

Divisors are the numbers that divide a given number exactlywith no remainder.

How many divisors does 72 have?

In totalit has twelve divisors (including one and itself). Not including itselfit has eleven proper divisors.

• Number of divisors d(n): 12
• Number of proper divisors τ(n)−1: 11

• List of divisors. Here is the complete set:

  1 2 3 4 6 8 9 12 18 24 36 72
• Sum of all divisors σ(n): 195
• Sum of proper divisors (its aliquot sum) s(n): 123
• 72 is an ‘abundant’ (or ‘excessive’) numberbecause the sum of its proper divisors (123) is greater than itself. Its abundance is 51

Roots and squares of 72

Roots of a number are numbers thatwhen multiplied by themselves a certain number of timesgive the original number. For examplethe square root of four is twobecause 2 × 2 = 4.

Squares are numbers obtained by multiplying a number by itself a certain number of times.

• 72 squared (72²) is 5184
• 72 cubed (72³) is 373248
• The square root of 72 is 8.49
• The cube root of 72 is 4.16

Scales and comparisons

How big is 72? The following comparisons will give you some idea.

• 72 seconds is equivalent to 1 minute and 12 seconds.

  Based on an average year length (including leap years) of ~365.24 days.

• How long would it take to count to 72?

  To count non-stop from 1 to 72 would take you approximately 36 seconds.

  This is a very rough estimatebased on a speaking rate of half a second every third order of magnitude. If you speak quicklyyou could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to sayso we add half a second for every extra ×1000. (We do not count involuntary pausesbathroom breaks or the necessity of sleep in our calculation!)

• A solid cube with a volume of 72 cubic inches would be around 4.16 inches high.

Fun! Recreational maths with 72

• 72 backwards is 27
• It has 2 decimal digits.
• If you add the digits together you get 9
• 72 is exactly divisible by the sum of its digits (9) in base 10. That means 72 is a Harshad number (aka Niven number).
• More fun facts coming soon.

Related numbers

Numbers related to 72.

• The previous prime number is 71
• The next prime number is 73
• 72 doubled equals 144

About this page

Data compiled by the Numbermatics team.

Page content last reviewed: 5 February 2026. Mathematical properties verified on 5 February 2026.