The number 3972
3972 is a composite number with 12 divisors. Its prime factorisation is × 3 × 331. Divisors (12): 1, 2, 3, 4, 6, 12, 331, 662, 993, 1324, 1986, 3972.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
3972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
3972 is composite. Its prime factorisation is
- 3
The divisors add up to 9296; without 3972 itself that is 5324, so 3972 is abundant (5324 is more than 3972). Euler's totient φ(3972) = 1320 numbers up to 3972 share no factor with it.
- 4
The digits of 3972 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 95 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3972 = 2^{2} \times 3 \times 331 \]3972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 9296 |
| Euler totient φ(n) | 1320 |
| Square | 15776784 |
| Cube | 62665386048 |
| Square root | 63.023805 (= 2√993) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 95 |
| Scientific notation | 3.972 × |
3972 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and seventy-two |
| Roman numerals | MMMCMLXXII |
| Binary (base 2) | 111110000100 |
| Octal (base 8) | 7604 |
| Hexadecimal (base 16) | F84 |
| Base 3 | 12110010 |
| As time | 3972 seconds = 1 h 6 min 12 s |
Is 3972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3972 ÷ 2 = 1986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3972 ÷ 3 = 1324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3972 ÷ 4 = 993) | 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 (3972 ÷ 6 = 662) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 3) | 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 (3972 ÷ 12 = 331) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3972 a prime number?
No. 3972 = × 3 × 331, so it is divisible by 2.
What are the factors of 3972?
1, 2, 3, 4, 6, 12, 331, 662, 993, 1324, 1986, 3972.
What is 3972 in binary?
111110000100 (hexadecimal F84, octal 7604).
What is the square root of 3972?
About 63.0238, exactly 2√993.
What is 3972 in Roman numerals?
MMMCMLXXII.
Is 3972 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 3972?
It is a composite number with 12 divisors.