The number 73980
73980 is a composite number with 48 divisors. Its prime factorisation is × × 5 × 137. Divisors (48): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45 … 73980.
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How to work it out
- 1
What is special about 73980: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
73980 is composite. Its prime factorisation is
- 3
The divisors add up to 231840; without 73980 itself that is 157860, so 73980 is abundant (157860 is more than 73980). Euler's totient φ(73980) = 19584 numbers up to 73980 share no factor with it.
- 4
The digits of 73980 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 187 steps to reach 1.
LaTeX source of the formulas on this page
\[ 73980 = 2^{2} \times 3^{3} \times 5 \times 137 \]73980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 231840 |
| Euler totient φ(n) | 19584 |
| Square | 5473040400 |
| Cube | 404895528792000 |
| Square root | 271.992647 (= 6√2055) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 187 |
| Scientific notation | 7.398 × |
73980 in other forms
| Form | Value |
|---|---|
| In words | seventy-three thousand nine hundred and eighty |
| Binary (base 2) | 10010000011111100 |
| Octal (base 8) | 220374 |
| Hexadecimal (base 16) | 120FC |
| Base 3 | 10202111000 |
| As time | 73980 seconds = 20 h 33 min 0 s |
Is 73980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (73980 ÷ 2 = 36990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (73980 ÷ 3 = 24660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (73980 ÷ 4 = 18495) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (73980 ÷ 5 = 14796) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (73980 ÷ 6 = 12330) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (73980 ÷ 9 = 8220) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (73980 ÷ 10 = 7398) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (73980 ÷ 12 = 6165) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 73980 a prime number?
No. 73980 = × × 5 × 137, so it is divisible by 2.
What are the factors of 73980?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 137, 180, 270, 274, 411, 540, 548, 685, 822, 1233, 1370, 1644, 2055, 2466, 2740, 3699, 4110, 4932, 6165, 7398, 8220, 12330, 14796, 18495, 24660, 36990, 73980.
What is 73980 in binary?
10010000011111100 (hexadecimal 120FC, octal 220374).
What is the square root of 73980?
About 271.9926, exactly 6√2055.
Is 73980 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 73980?
73980 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.