The number 40224
40224 is a composite number with 24 divisors. Its prime factorisation is × 3 × 419. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 419, 838, 1257, 1676 … 40224.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40224: a Harshad number: divisible by its digit sum 12.
- 2
40224 is composite. Its prime factorisation is
- 3
The divisors add up to 105840; without 40224 itself that is 65616, so 40224 is abundant (65616 is more than 40224). Euler's totient φ(40224) = 13376 numbers up to 40224 share no factor with it.
- 4
The digits of 40224 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40224 = 2^{5} \times 3 \times 419 \]40224 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 105840 |
| Euler totient φ(n) | 13376 |
| Square | 1617970176 |
| Cube | 65081232359424 |
| Square root | 200.559218 (= 4√2514) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.0224 × |
40224 in other forms
| Form | Value |
|---|---|
| In words | forty thousand two hundred and twenty-four |
| Binary (base 2) | 1001110100100000 |
| Octal (base 8) | 116440 |
| Hexadecimal (base 16) | 9D20 |
| Base 3 | 2001011210 |
| As time | 40224 seconds = 11 h 10 min 24 s |
Is 40224 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40224 ÷ 2 = 20112) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40224 ÷ 3 = 13408) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40224 ÷ 4 = 10056) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (40224 ÷ 6 = 6704) | 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 | Yes (40224 ÷ 8 = 5028) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (40224 ÷ 12 = 3352) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40224 a prime number?
No. 40224 = × 3 × 419, so it is divisible by 2.
What are the factors of 40224?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 419, 838, 1257, 1676, 2514, 3352, 5028, 6704, 10056, 13408, 20112, 40224.
What is 40224 in binary?
1001110100100000 (hexadecimal 9D20, octal 116440).
What is the square root of 40224?
About 200.5592, exactly 4√2514.
Is 40224 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 40224?
40224 is a Harshad number: divisible by its digit sum 12.