The number 37920
37920 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 79. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 37920.
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How to work it out
- 1
37920 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
37920 is composite. Its prime factorisation is
- 3
The divisors add up to 120960; without 37920 itself that is 83040, so 37920 is abundant (83040 is more than 37920). Euler's totient φ(37920) = 9984 numbers up to 37920 share no factor with it.
- 4
The digits of 37920 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 155 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37920 = 2^{5} \times 3 \times 5 \times 79 \]37920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 120960 |
| Euler totient φ(n) | 9984 |
| Square | 1437926400 |
| Cube | 54526169088000 |
| Square root | 194.730583 (= 4√2370) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 155 |
| Scientific notation | 3.792 × |
37920 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand nine hundred and twenty |
| Binary (base 2) | 1001010000100000 |
| Octal (base 8) | 112040 |
| Hexadecimal (base 16) | 9420 |
| Base 3 | 1221000110 |
| As time | 37920 seconds = 10 h 32 min 0 s |
Is 37920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37920 ÷ 2 = 18960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37920 ÷ 3 = 12640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37920 ÷ 4 = 9480) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (37920 ÷ 5 = 7584) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37920 ÷ 6 = 6320) | 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 (37920 ÷ 8 = 4740) | 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 (37920 ÷ 10 = 3792) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (37920 ÷ 12 = 3160) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37920 a prime number?
No. 37920 = × 3 × 5 × 79, so it is divisible by 2.
What are the factors of 37920?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 79, 80, 96, 120, 158, 160, 237, 240, 316, 395, 474, 480, 632, 790, 948, 1185, 1264, 1580, 1896, 2370, 2528, 3160, 3792, 4740, 6320, 7584, 9480, 12640, 18960, 37920.
What is 37920 in binary?
1001010000100000 (hexadecimal 9420, octal 112040).
What is the square root of 37920?
About 194.7306, exactly 4√2370.
Is 37920 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 37920?
It is a composite number with 48 divisors.