The number 3948
3948 is a composite number with 24 divisors. Its prime factorisation is × 3 × 7 × 47. Divisors (24): 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 47, 84, 94, 141, 188 … 3948.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
3948 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
3948 is composite. Its prime factorisation is
- 3
The divisors add up to 10752; without 3948 itself that is 6804, so 3948 is abundant (6804 is more than 3948). Euler's totient φ(3948) = 1104 numbers up to 3948 share no factor with it.
- 4
The digits of 3948 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3948 = 2^{2} \times 3 \times 7 \times 47 \]3948 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 10752 |
| Euler totient φ(n) | 1104 |
| Square | 15586704 |
| Cube | 61536307392 |
| Square root | 62.833112 (= 2√987) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 38 |
| Scientific notation | 3.948 × |
3948 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and forty-eight |
| Roman numerals | MMMCMXLVIII |
| Binary (base 2) | 111101101100 |
| Octal (base 8) | 7554 |
| Hexadecimal (base 16) | F6C |
| Base 3 | 12102020 |
| As time | 3948 seconds = 1 h 5 min 48 s |
Is 3948 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3948 ÷ 2 = 1974) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3948 ÷ 3 = 1316) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3948 ÷ 4 = 987) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3948 ÷ 6 = 658) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (3948 ÷ 7 = 564) | 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 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 (3948 ÷ 12 = 329) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3948 a prime number?
No. 3948 = × 3 × 7 × 47, so it is divisible by 2.
What are the factors of 3948?
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 47, 84, 94, 141, 188, 282, 329, 564, 658, 987, 1316, 1974, 3948.
What is 3948 in binary?
111101101100 (hexadecimal F6C, octal 7554).
What is the square root of 3948?
About 62.8331, exactly 2√987.
What is 3948 in Roman numerals?
MMMCMXLVIII.
Is 3948 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 3948?
It is a composite number with 24 divisors.