The number 36972
36972 is a composite number with 36 divisors. Its prime factorisation is × × 13 × 79. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 79, 117 … 36972.
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How to work it out
- 1
36972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
36972 is composite. Its prime factorisation is
- 3
The divisors add up to 101920; without 36972 itself that is 64948, so 36972 is abundant (64948 is more than 36972). Euler's totient φ(36972) = 11232 numbers up to 36972 share no factor with it.
- 4
The digits of 36972 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 36972 = 2^{2} \times 3^{2} \times 13 \times 79 \]36972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 101920 |
| Euler totient φ(n) | 11232 |
| Square | 1366928784 |
| Cube | 50538091002048 |
| Square root | 192.281044 (= 6√1027) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 93 |
| Scientific notation | 3.6972 × |
36972 in other forms
| Form | Value |
|---|---|
| In words | thirty-six thousand nine hundred and seventy-two |
| Binary (base 2) | 1001000001101100 |
| Octal (base 8) | 110154 |
| Hexadecimal (base 16) | 906C |
| Base 3 | 1212201100 |
| As time | 36972 seconds = 10 h 16 min 12 s |
Is 36972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (36972 ÷ 2 = 18486) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (36972 ÷ 3 = 12324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (36972 ÷ 4 = 9243) | 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 (36972 ÷ 6 = 6162) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (36972 ÷ 9 = 4108) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (36972 ÷ 12 = 3081) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 36972 a prime number?
No. 36972 = × × 13 × 79, so it is divisible by 2.
What are the factors of 36972?
1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 79, 117, 156, 158, 234, 237, 316, 468, 474, 711, 948, 1027, 1422, 2054, 2844, 3081, 4108, 6162, 9243, 12324, 18486, 36972.
What is 36972 in binary?
1001000001101100 (hexadecimal 906C, octal 110154).
What is the square root of 36972?
About 192.2810, exactly 6√1027.
Is 36972 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 36972?
It is a composite number with 36 divisors.