The number 3969
3969 is a perfect square (63²). Its prime factorisation is × . Divisors (15): 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3969: a perfect square (63²); a Harshad number: divisible by its digit sum 27.
- 2
3969 is composite. Its prime factorisation is
- 3
The divisors add up to 6897; without 3969 itself that is 2928, so 3969 is deficient (2928 is less than 3969). Euler's totient φ(3969) = 2268 numbers up to 3969 share no factor with it.
- 4
The digits of 3969 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 144 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3969 = 3^{4} \times 7^{2} \]3969 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 6897 |
| Euler totient φ(n) | 2268 |
| Square | 15752961 |
| Cube | 62523502209 |
| Square root | 63 |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 144 |
| Scientific notation | 3.969 × |
| Perfect power |
3969 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and sixty-nine |
| Roman numerals | MMMCMLXIX |
| Binary (base 2) | 111110000001 |
| Octal (base 8) | 7601 |
| Hexadecimal (base 16) | F81 |
| Base 3 | 12110000 |
| As time | 3969 seconds = 1 h 6 min 9 s |
Is 3969 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 (3969 ÷ 3 = 1323) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | 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 | Yes (3969 ÷ 7 = 567) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3969 ÷ 9 = 441) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3969 a prime number?
No. 3969 = × , so it is divisible by 3.
What are the factors of 3969?
1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969.
What is 3969 in binary?
111110000001 (hexadecimal F81, octal 7601).
What is the square root of 3969?
63, because 63 × 63 = 3969.
What is 3969 in Roman numerals?
MMMCMLXIX.
Is 3969 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 3969?
3969 is a perfect square (63²); a Harshad number: divisible by its digit sum 27.