The number 37820
37820 is a composite number with 24 divisors. Its prime factorisation is × 5 × 31 × 61. Divisors (24): 1, 2, 4, 5, 10, 20, 31, 61, 62, 122, 124, 155, 244, 305, 310, 610 … 37820.
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How to work it out
- 1
What is special about 37820: a Harshad number: divisible by its digit sum 20.
- 2
37820 is composite. Its prime factorisation is
- 3
The divisors add up to 83328; without 37820 itself that is 45508, so 37820 is abundant (45508 is more than 37820). Euler's totient φ(37820) = 14400 numbers up to 37820 share no factor with it.
- 4
The digits of 37820 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 155 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37820 = 2^{2} \times 5 \times 31 \times 61 \]37820 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 83328 |
| Euler totient φ(n) | 14400 |
| Square | 1430352400 |
| Cube | 54095927768000 |
| Square root | 194.473649 (= 2√9455) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 155 |
| Scientific notation | 3.782 × |
37820 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand eight hundred and twenty |
| Binary (base 2) | 1001001110111100 |
| Octal (base 8) | 111674 |
| Hexadecimal (base 16) | 93BC |
| Base 3 | 1220212202 |
| As time | 37820 seconds = 10 h 30 min 20 s |
Is 37820 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37820 ÷ 2 = 18910) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37820 ÷ 4 = 9455) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (37820 ÷ 5 = 7564) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (37820 ÷ 10 = 3782) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37820 a prime number?
No. 37820 = × 5 × 31 × 61, so it is divisible by 2.
What are the factors of 37820?
1, 2, 4, 5, 10, 20, 31, 61, 62, 122, 124, 155, 244, 305, 310, 610, 620, 1220, 1891, 3782, 7564, 9455, 18910, 37820.
What is 37820 in binary?
1001001110111100 (hexadecimal 93BC, octal 111674).
What is the square root of 37820?
About 194.4736, exactly 2√9455.
Is 37820 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 37820?
37820 is a Harshad number: divisible by its digit sum 20.