The number 67980
67980 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 11 × 103. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55 … 67980.
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How to work it out
- 1
What is special about 67980: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.
- 2
67980 is composite. Its prime factorisation is
- 3
The divisors add up to 209664; without 67980 itself that is 141684, so 67980 is abundant (141684 is more than 67980). Euler's totient φ(67980) = 16320 numbers up to 67980 share no factor with it.
- 4
The digits of 67980 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 130 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67980 = 2^{2} \times 3 \times 5 \times 11 \times 103 \]67980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 209664 |
| Euler totient φ(n) | 16320 |
| Square | 4621280400 |
| Cube | 314154641592000 |
| Square root | 260.729745 (= 2√16995) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 130 |
| Scientific notation | 6.798 × |
67980 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand nine hundred and eighty |
| Binary (base 2) | 10000100110001100 |
| Octal (base 8) | 204614 |
| Hexadecimal (base 16) | 1098C |
| Base 3 | 10110020210 |
| As time | 67980 seconds = 18 h 53 min 0 s |
Is 67980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67980 ÷ 2 = 33990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67980 ÷ 3 = 22660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67980 ÷ 4 = 16995) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (67980 ÷ 5 = 13596) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (67980 ÷ 6 = 11330) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (67980 ÷ 10 = 6798) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (67980 ÷ 11 = 6180) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (67980 ÷ 12 = 5665) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67980 a prime number?
No. 67980 = × 3 × 5 × 11 × 103, so it is divisible by 2.
What are the factors of 67980?
1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 103, 110, 132, 165, 206, 220, 309, 330, 412, 515, 618, 660, 1030, 1133, 1236, 1545, 2060, 2266, 3090, 3399, 4532, 5665, 6180, 6798, 11330, 13596, 16995, 22660, 33990, 67980.
What is 67980 in binary?
10000100110001100 (hexadecimal 1098C, octal 204614).
What is the square root of 67980?
About 260.7297, exactly 2√16995.
Is 67980 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 67980?
67980 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.