The number 37380
37380 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 7 × 89. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35 … 37380.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37380: a Harshad number: divisible by its digit sum 21.
- 2
37380 is composite. Its prime factorisation is
- 3
The divisors add up to 120960; without 37380 itself that is 83580, so 37380 is abundant (83580 is more than 37380). Euler's totient φ(37380) = 8448 numbers up to 37380 share no factor with it.
- 4
The digits of 37380 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 186 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37380 = 2^{2} \times 3 \times 5 \times 7 \times 89 \]37380 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 120960 |
| Euler totient φ(n) | 8448 |
| Square | 1397264400 |
| Cube | 52229743272000 |
| Square root | 193.339080 (= 2√9345) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 186 |
| Scientific notation | 3.738 × |
37380 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand three hundred and eighty |
| Binary (base 2) | 1001001000000100 |
| Octal (base 8) | 111004 |
| Hexadecimal (base 16) | 9204 |
| Base 3 | 1220021110 |
| As time | 37380 seconds = 10 h 23 min 0 s |
Is 37380 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37380 ÷ 2 = 18690) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37380 ÷ 3 = 12460) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37380 ÷ 4 = 9345) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (37380 ÷ 5 = 7476) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37380 ÷ 6 = 6230) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (37380 ÷ 7 = 5340) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (37380 ÷ 10 = 3738) | 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 | Yes (37380 ÷ 12 = 3115) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37380 a prime number?
No. 37380 = × 3 × 5 × 7 × 89, so it is divisible by 2.
What are the factors of 37380?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 89, 105, 140, 178, 210, 267, 356, 420, 445, 534, 623, 890, 1068, 1246, 1335, 1780, 1869, 2492, 2670, 3115, 3738, 5340, 6230, 7476, 9345, 12460, 18690, 37380.
What is 37380 in binary?
1001001000000100 (hexadecimal 9204, octal 111004).
What is the square root of 37380?
About 193.3391, exactly 2√9345.
Is 37380 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 37380?
37380 is a Harshad number: divisible by its digit sum 21.