The number 7842
7842 is a composite number with 8 divisors. Its prime factorisation is 2 × 3 × 1307. Divisors (8): 1, 2, 3, 6, 1307, 2614, 3921, 7842.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7842: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
7842 is composite. Its prime factorisation is
- 3
The divisors add up to 15696; without 7842 itself that is 7854, so 7842 is abundant (7854 is more than 7842). Euler's totient φ(7842) = 2612 numbers up to 7842 share no factor with it.
- 4
The digits of 7842 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 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7842 = 2 \times 3 \times 1307 \]
7842 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 15696 |
| Euler totient φ(n) | 2612 |
| Square | 61496964 |
| Cube | 482259191688 |
| Square root | 88.555068 |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 52 |
| Scientific notation | 7.842 × |
7842 in other forms
| Form | Value |
|---|---|
| In words | seven thousand eight hundred and forty-two |
| Binary (base 2) | 1111010100010 |
| Octal (base 8) | 17242 |
| Hexadecimal (base 16) | 1EA2 |
| Base 3 | 101202110 |
| As time | 7842 seconds = 2 h 10 min 42 s |
Is 7842 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7842 ÷ 2 = 3921) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7842 ÷ 3 = 2614) | 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 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7842 ÷ 6 = 1307) | 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 | 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 10) | 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 7842 a prime number?
No. 7842 = 2 × 3 × 1307, so it is divisible by 2.
What are the factors of 7842?
1, 2, 3, 6, 1307, 2614, 3921, 7842.
What is 7842 in binary?
1111010100010 (hexadecimal 1EA2, octal 17242).
What is the square root of 7842?
About 88.5551.
Is 7842 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 7842?
7842 is a happy number: repeatedly adding the squares of its digits reaches 1.