The number 40200
40200 is a composite number with 48 divisors. Its prime factorisation is × 3 × × 67. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50 … 40200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40200: a Harshad number: divisible by its digit sum 6.
- 2
40200 is composite. Its prime factorisation is
- 3
The divisors add up to 126480; without 40200 itself that is 86280, so 40200 is abundant (86280 is more than 40200). Euler's totient φ(40200) = 10560 numbers up to 40200 share no factor with it.
- 4
The digits of 40200 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 119 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40200 = 2^{3} \times 3 \times 5^{2} \times 67 \]40200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 126480 |
| Euler totient φ(n) | 10560 |
| Square | 1616040000 |
| Cube | 64964808000000 |
| Square root | 200.499377 (= 10√402) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 119 |
| Scientific notation | 4.02 × |
40200 in other forms
| Form | Value |
|---|---|
| In words | forty thousand two hundred |
| Binary (base 2) | 1001110100001000 |
| Octal (base 8) | 116410 |
| Hexadecimal (base 16) | 9D08 |
| Base 3 | 2001010220 |
| As time | 40200 seconds = 11 h 10 min 0 s |
Is 40200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40200 ÷ 2 = 20100) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40200 ÷ 3 = 13400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40200 ÷ 4 = 10050) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (40200 ÷ 5 = 8040) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (40200 ÷ 6 = 6700) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (40200 ÷ 8 = 5025) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (40200 ÷ 10 = 4020) | 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 | Yes (40200 ÷ 12 = 3350) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40200 a prime number?
No. 40200 = × 3 × × 67, so it is divisible by 2.
What are the factors of 40200?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 67, 75, 100, 120, 134, 150, 200, 201, 268, 300, 335, 402, 536, 600, 670, 804, 1005, 1340, 1608, 1675, 2010, 2680, 3350, 4020, 5025, 6700, 8040, 10050, 13400, 20100, 40200.
What is 40200 in binary?
1001110100001000 (hexadecimal 9D08, octal 116410).
What is the square root of 40200?
About 200.4994, exactly 10√402.
Is 40200 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 40200?
40200 is a Harshad number: divisible by its digit sum 6.