The number 1971
1971 is a composite number with 8 divisors. Its prime factorisation is × 73. Divisors (8): 1, 3, 9, 27, 73, 219, 657, 1971.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1971 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1971 is composite. Its prime factorisation is
- 3
The divisors add up to 2960; without 1971 itself that is 989, so 1971 is deficient (989 is less than 1971). Euler's totient φ(1971) = 1296 numbers up to 1971 share no factor with it.
- 4
The digits of 1971 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1971 = 3^{3} \times 73 \]1971 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2960 |
| Euler totient φ(n) | 1296 |
| Square | 3884841 |
| Cube | 7657021611 |
| Square root | 44.395946 (= 3√219) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 24 |
| Scientific notation | 1.971 × |
1971 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and seventy-one |
| Roman numerals | MCMLXXI |
| Binary (base 2) | 11110110011 |
| Octal (base 8) | 3663 |
| Hexadecimal (base 16) | 7B3 |
| Base 3 | 2201000 |
| As time | 1971 seconds = 32 min 51 s |
Is 1971 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1971 ÷ 3 = 657) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1971 ÷ 9 = 219) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1971 a prime number?
No. 1971 = × 73, so it is divisible by 3.
What are the factors of 1971?
1, 3, 9, 27, 73, 219, 657, 1971.
What is 1971 in binary?
11110110011 (hexadecimal 7B3, octal 3663).
What is the square root of 1971?
About 44.3959, exactly 3√219.
What is 1971 in Roman numerals?
MCMLXXI.
Is 1971 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1971?
It is a composite number with 8 divisors.