The number 72
72 is a composite number with 12 divisors. Its prime factorisation is × . Divisors (12): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72: a Harshad number: divisible by its digit sum 9.
- 2
72 is composite. Its prime factorisation is
- 3
The divisors add up to 195; without 72 itself that is 123, so 72 is abundant (123 is more than 72). Euler's totient φ(72) = 24 numbers up to 72 share no factor with it.
- 4
The digits of 72 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 22 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72 = 2^{3} \times 3^{2} \]72 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 195 |
| Euler totient φ(n) | 24 |
| Square | 5184 |
| Cube | 373248 |
| Square root | 8.485281 (= 6√2) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 22 |
| Scientific notation | 7.2 × |
72 in other forms
| Form | Value |
|---|---|
| In words | seventy-two |
| Roman numerals | LXXII |
| Binary (base 2) | 1001000 |
| Octal (base 8) | 110 |
| Hexadecimal (base 16) | 48 |
| Base 3 | 2200 |
| As time | 72 seconds = 1 min 12 s |
Is 72 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72 ÷ 2 = 36) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72 ÷ 3 = 24) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72 ÷ 4 = 18) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72 ÷ 6 = 12) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (72 ÷ 8 = 9) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72 ÷ 9 = 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72 ÷ 12 = 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72 a prime number?
No. 72 = × , so it is divisible by 2.
What are the factors of 72?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
What is 72 in binary?
1001000 (hexadecimal 48, octal 110).
What is the square root of 72?
About 8.4853, exactly 6√2.
What is 72 in Roman numerals?
LXXII.
Is 72 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 72?
72 is a Harshad number: divisible by its digit sum 9.