The number 37980
37980 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 211. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 37980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37980: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
37980 is composite. Its prime factorisation is
- 3
The divisors add up to 115752; without 37980 itself that is 77772, so 37980 is abundant (77772 is more than 37980). Euler's totient φ(37980) = 10080 numbers up to 37980 share no factor with it.
- 4
The digits of 37980 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 155 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37980 = 2^{2} \times 3^{2} \times 5 \times 211 \]37980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 115752 |
| Euler totient φ(n) | 10080 |
| Square | 1442480400 |
| Cube | 54785405592000 |
| Square root | 194.884581 (= 6√1055) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 155 |
| Scientific notation | 3.798 × |
37980 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand nine hundred and eighty |
| Binary (base 2) | 1001010001011100 |
| Octal (base 8) | 112134 |
| Hexadecimal (base 16) | 945C |
| Base 3 | 1221002200 |
| As time | 37980 seconds = 10 h 33 min 0 s |
Is 37980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37980 ÷ 2 = 18990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37980 ÷ 3 = 12660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37980 ÷ 4 = 9495) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (37980 ÷ 5 = 7596) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37980 ÷ 6 = 6330) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | Yes (37980 ÷ 9 = 4220) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (37980 ÷ 10 = 3798) | 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 (37980 ÷ 12 = 3165) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37980 a prime number?
No. 37980 = × × 5 × 211, so it is divisible by 2.
What are the factors of 37980?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 211, 422, 633, 844, 1055, 1266, 1899, 2110, 2532, 3165, 3798, 4220, 6330, 7596, 9495, 12660, 18990, 37980.
What is 37980 in binary?
1001010001011100 (hexadecimal 945C, octal 112134).
What is the square root of 37980?
About 194.8846, exactly 6√1055.
Is 37980 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 37980?
37980 is a happy number: repeatedly adding the squares of its digits reaches 1.