The number 5978
5978 is a composite number with 12 divisors. Its prime factorisation is 2 × × 61. Divisors (12): 1, 2, 7, 14, 49, 61, 98, 122, 427, 854, 2989, 5978.
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How to work it out
- 1
What is special about 5978: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
5978 is composite. Its prime factorisation is
- 3
The divisors add up to 10602; without 5978 itself that is 4624, so 5978 is deficient (4624 is less than 5978). Euler's totient φ(5978) = 2520 numbers up to 5978 share no factor with it.
- 4
The digits of 5978 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5978 = 2 \times 7^{2} \times 61 \]5978 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 10602 |
| Euler totient φ(n) | 2520 |
| Square | 35736484 |
| Cube | 213632701352 |
| Square root | 77.317527 (= 7√122) |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 49 |
| Scientific notation | 5.978 × |
5978 in other forms
| Form | Value |
|---|---|
| In words | five thousand nine hundred and seventy-eight |
| Binary (base 2) | 1011101011010 |
| Octal (base 8) | 13532 |
| Hexadecimal (base 16) | 175A |
| Base 3 | 22012102 |
| As time | 5978 seconds = 1 h 39 min 38 s |
Is 5978 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5978 ÷ 2 = 2989) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (5978 ÷ 7 = 854) | 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 | No (remainder 2) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5978 a prime number?
No. 5978 = 2 × × 61, so it is divisible by 2.
What are the factors of 5978?
1, 2, 7, 14, 49, 61, 98, 122, 427, 854, 2989, 5978.
What is 5978 in binary?
1011101011010 (hexadecimal 175A, octal 13532).
What is the square root of 5978?
About 77.3175, exactly 7√122.
Is 5978 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 5978?
5978 is a happy number: repeatedly adding the squares of its digits reaches 1.