The number 8442
8442 is a composite number with 24 divisors. Its prime factorisation is 2 × × 7 × 67. Divisors (24): 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 67, 126, 134, 201, 402 … 8442.
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How to work it out
- 1
What is special about 8442: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
8442 is composite. Its prime factorisation is
- 3
The divisors add up to 21216; without 8442 itself that is 12774, so 8442 is abundant (12774 is more than 8442). Euler's totient φ(8442) = 2376 numbers up to 8442 share no factor with it.
- 4
The digits of 8442 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 171 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8442 = 2 \times 3^{2} \times 7 \times 67 \]8442 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 21216 |
| Euler totient φ(n) | 2376 |
| Square | 71267364 |
| Cube | 601639086888 |
| Square root | 91.880357 (= 3√938) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 171 |
| Scientific notation | 8.442 × |
8442 in other forms
| Form | Value |
|---|---|
| In words | eight thousand four hundred and forty-two |
| Binary (base 2) | 10000011111010 |
| Octal (base 8) | 20372 |
| Hexadecimal (base 16) | 20FA |
| Base 3 | 102120200 |
| As time | 8442 seconds = 2 h 20 min 42 s |
Is 8442 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8442 ÷ 2 = 4221) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8442 ÷ 3 = 2814) | 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 (8442 ÷ 6 = 1407) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (8442 ÷ 7 = 1206) | 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 (8442 ÷ 9 = 938) | 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 5) | 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 8442 a prime number?
No. 8442 = 2 × × 7 × 67, so it is divisible by 2.
What are the factors of 8442?
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 67, 126, 134, 201, 402, 469, 603, 938, 1206, 1407, 2814, 4221, 8442.
What is 8442 in binary?
10000011111010 (hexadecimal 20FA, octal 20372).
What is the square root of 8442?
About 91.8804, exactly 3√938.
Is 8442 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 8442?
8442 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.