The number 42672
42672 is a composite number with 40 divisors. Its prime factorisation is × 3 × 7 × 127. Divisors (40): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56 … 42672.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 42672: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
42672 is composite. Its prime factorisation is
- 3
The divisors add up to 126976; without 42672 itself that is 84304, so 42672 is abundant (84304 is more than 42672). Euler's totient φ(42672) = 12096 numbers up to 42672 share no factor with it.
- 4
The digits of 42672 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 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 42672 = 2^{4} \times 3 \times 7 \times 127 \]42672 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 126976 |
| Euler totient φ(n) | 12096 |
| Square | 1820899584 |
| Cube | 77701427048448 |
| Square root | 206.572021 (= 4√2667) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 49 |
| Scientific notation | 4.2672 × |
42672 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand six hundred and seventy-two |
| Binary (base 2) | 1010011010110000 |
| Octal (base 8) | 123260 |
| Hexadecimal (base 16) | A6B0 |
| Base 3 | 2011112110 |
| As time | 42672 seconds = 11 h 51 min 12 s |
Is 42672 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (42672 ÷ 2 = 21336) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (42672 ÷ 3 = 14224) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (42672 ÷ 4 = 10668) | 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 (42672 ÷ 6 = 7112) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (42672 ÷ 7 = 6096) | 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 | Yes (42672 ÷ 8 = 5334) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (42672 ÷ 12 = 3556) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 42672 a prime number?
No. 42672 = × 3 × 7 × 127, so it is divisible by 2.
What are the factors of 42672?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 127, 168, 254, 336, 381, 508, 762, 889, 1016, 1524, 1778, 2032, 2667, 3048, 3556, 5334, 6096, 7112, 10668, 14224, 21336, 42672.
What is 42672 in binary?
1010011010110000 (hexadecimal A6B0, octal 123260).
What is the square root of 42672?
About 206.5720, exactly 4√2667.
Is 42672 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 42672?
42672 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.