The number 3978
3978 is a composite number with 24 divisors. Its prime factorisation is 2 × × 13 × 17. Divisors (24): 1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153 … 3978.
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How to work it out
- 1
What is special about 3978: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
3978 is composite. Its prime factorisation is
- 3
The divisors add up to 9828; without 3978 itself that is 5850, so 3978 is abundant (5850 is more than 3978). Euler's totient φ(3978) = 1152 numbers up to 3978 share no factor with it.
- 4
The digits of 3978 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 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3978 = 2 \times 3^{2} \times 13 \times 17 \]3978 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 9828 |
| Euler totient φ(n) | 1152 |
| Square | 15824484 |
| Cube | 62949797352 |
| Square root | 63.071388 (= 3√442) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 25 |
| Scientific notation | 3.978 × |
3978 in other forms
| Form | Value |
|---|---|
| In words | three thousand nine hundred and seventy-eight |
| Roman numerals | MMMCMLXXVIII |
| Binary (base 2) | 111110001010 |
| Octal (base 8) | 7612 |
| Hexadecimal (base 16) | F8A |
| Base 3 | 12110100 |
| As time | 3978 seconds = 1 h 6 min 18 s |
Is 3978 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3978 ÷ 2 = 1989) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3978 ÷ 3 = 1326) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | 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 (3978 ÷ 6 = 663) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (3978 ÷ 9 = 442) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3978 a prime number?
No. 3978 = 2 × × 13 × 17, so it is divisible by 2.
What are the factors of 3978?
1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 221, 234, 306, 442, 663, 1326, 1989, 3978.
What is 3978 in binary?
111110001010 (hexadecimal F8A, octal 7612).
What is the square root of 3978?
About 63.0714, exactly 3√442.
What is 3978 in Roman numerals?
MMMCMLXXVIII.
Is 3978 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 3978?
3978 is a happy number: repeatedly adding the squares of its digits reaches 1.