The number 27972
27972 is a palindrome: it reads 27972 backwards too. Its prime factorisation is × × 7 × 37. Divisors (48): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 37, 42 … 27972.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27972: a palindrome: it reads 27972 backwards too; a Harshad number: divisible by its digit sum 27.
- 2
27972 is composite. Its prime factorisation is
- 3
The divisors add up to 85120; without 27972 itself that is 57148, so 27972 is abundant (57148 is more than 27972). Euler's totient φ(27972) = 7776 numbers up to 27972 share no factor with it.
- 4
The digits of 27972 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 108 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27972 = 2^{2} \times 3^{3} \times 7 \times 37 \]27972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 85120 |
| Euler totient φ(n) | 7776 |
| Square | 782432784 |
| Cube | 21886209834048 |
| Square root | 167.248318 (= 6√777) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 108 |
| Scientific notation | 2.7972 × |
27972 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand nine hundred and seventy-two |
| Binary (base 2) | 110110101000100 |
| Octal (base 8) | 66504 |
| Hexadecimal (base 16) | 6D44 |
| Base 3 | 1102101000 |
| As time | 27972 seconds = 7 h 46 min 12 s |
Is 27972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27972 ÷ 2 = 13986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27972 ÷ 3 = 9324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27972 ÷ 4 = 6993) | 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 (27972 ÷ 6 = 4662) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (27972 ÷ 7 = 3996) | 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 (27972 ÷ 9 = 3108) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27972 ÷ 12 = 2331) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27972 a prime number?
No. 27972 = × × 7 × 37, so it is divisible by 2.
What are the factors of 27972?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 37, 42, 54, 63, 74, 84, 108, 111, 126, 148, 189, 222, 252, 259, 333, 378, 444, 518, 666, 756, 777, 999, 1036, 1332, 1554, 1998, 2331, 3108, 3996, 4662, 6993, 9324, 13986, 27972.
What is 27972 in binary?
110110101000100 (hexadecimal 6D44, octal 66504).
What is the square root of 27972?
About 167.2483, exactly 6√777.
Is 27972 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 27972?
27972 is a palindrome: it reads 27972 backwards too; a Harshad number: divisible by its digit sum 27.