The number 36
36 is a highly composite number: it has 9 divisors, more than any smaller number, a perfect square (6²) and a triangular number: 1 + 2 + … + 8 = 36. Its prime factorisation is × . Divisors (9): 1, 2, 3, 4, 6, 9, 12, 18, 36.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 36: a highly composite number: it has 9 divisors, more than any smaller number; a perfect square (6²); a triangular number: 1 + 2 + … + 8 = 36; a Harshad number: divisible by its digit sum 9.
- 2
36 is composite. Its prime factorisation is
- 3
The divisors add up to 91; without 36 itself that is 55, so 36 is abundant (55 is more than 36). Euler's totient φ(36) = 12 numbers up to 36 share no factor with it.
- 4
The digits of 36 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 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 36 = 2^{2} \times 3^{2} \]36 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 9 |
| Sum of divisors | 91 |
| Euler totient φ(n) | 12 |
| Square | 1296 |
| Cube | 46656 |
| Square root | 6 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 21 |
| Scientific notation | 3.6 × |
| Perfect power |
36 in other forms
| Form | Value |
|---|---|
| In words | thirty-six |
| Roman numerals | XXXVI |
| Binary (base 2) | 100100 |
| Octal (base 8) | 44 |
| Hexadecimal (base 16) | 24 |
| Base 3 | 1100 |
| As time | 36 seconds |
Is 36 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (36 ÷ 2 = 18) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (36 ÷ 3 = 12) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (36 ÷ 4 = 9) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (36 ÷ 6 = 6) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (36 ÷ 9 = 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (36 ÷ 12 = 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 36 a prime number?
No. 36 = × , so it is divisible by 2.
What are the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18, 36.
What is 36 in binary?
100100 (hexadecimal 24, octal 44).
What is the square root of 36?
6, because 6 × 6 = 36.
What is 36 in Roman numerals?
XXXVI.
Is 36 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 36?
36 is a highly composite number: it has 9 divisors, more than any smaller number; a perfect square (6²); a triangular number: 1 + 2 + … + 8 = 36; a Harshad number: divisible by its digit sum 9.