The number 42400
42400 is a composite number with 36 divisors. Its prime factorisation is × × 53. Divisors (36): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 53, 80, 100, 106 … 42400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 42400: a Harshad number: divisible by its digit sum 10.
- 2
42400 is composite. Its prime factorisation is
- 3
The divisors add up to 105462; without 42400 itself that is 63062, so 42400 is abundant (63062 is more than 42400). Euler's totient φ(42400) = 16640 numbers up to 42400 share no factor with it.
- 4
The digits of 42400 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 31 steps to reach 1.
LaTeX source of the formulas on this page
\[ 42400 = 2^{5} \times 5^{2} \times 53 \]42400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 105462 |
| Euler totient φ(n) | 16640 |
| Square | 1797760000 |
| Cube | 76225024000000 |
| Square root | 205.912603 (= 20√106) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 31 |
| Scientific notation | 4.24 × |
42400 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand four hundred |
| Binary (base 2) | 1010010110100000 |
| Octal (base 8) | 122640 |
| Hexadecimal (base 16) | A5A0 |
| Base 3 | 2011011101 |
| As time | 42400 seconds = 11 h 46 min 40 s |
Is 42400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (42400 ÷ 2 = 21200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (42400 ÷ 4 = 10600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (42400 ÷ 5 = 8480) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (42400 ÷ 8 = 5300) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (42400 ÷ 10 = 4240) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 42400 a prime number?
No. 42400 = × × 53, so it is divisible by 2.
What are the factors of 42400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 53, 80, 100, 106, 160, 200, 212, 265, 400, 424, 530, 800, 848, 1060, 1325, 1696, 2120, 2650, 4240, 5300, 8480, 10600, 21200, 42400.
What is 42400 in binary?
1010010110100000 (hexadecimal A5A0, octal 122640).
What is the square root of 42400?
About 205.9126, exactly 20√106.
Is 42400 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 42400?
42400 is a Harshad number: divisible by its digit sum 10.