The number 76980
76980 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 1283. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1283, 2566, 3849, 5132 … 76980.
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How to work it out
- 1
What is special about 76980: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.
- 2
76980 is composite. Its prime factorisation is
- 3
The divisors add up to 215712; without 76980 itself that is 138732, so 76980 is abundant (138732 is more than 76980). Euler's totient φ(76980) = 20512 numbers up to 76980 share no factor with it.
- 4
The digits of 76980 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 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 76980 = 2^{2} \times 3 \times 5 \times 1283 \]76980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 215712 |
| Euler totient φ(n) | 20512 |
| Square | 5925920400 |
| Cube | 456177352392000 |
| Square root | 277.452699 (= 2√19245) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.698 × |
76980 in other forms
| Form | Value |
|---|---|
| In words | seventy-six thousand nine hundred and eighty |
| Binary (base 2) | 10010110010110100 |
| Octal (base 8) | 226264 |
| Hexadecimal (base 16) | 12CB4 |
| Base 3 | 10220121010 |
| As time | 76980 seconds = 21 h 23 min 0 s |
Is 76980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (76980 ÷ 2 = 38490) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (76980 ÷ 3 = 25660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (76980 ÷ 4 = 19245) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (76980 ÷ 5 = 15396) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (76980 ÷ 6 = 12830) | 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 | 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 (76980 ÷ 10 = 7698) | 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 (76980 ÷ 12 = 6415) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 76980 a prime number?
No. 76980 = × 3 × 5 × 1283, so it is divisible by 2.
What are the factors of 76980?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1283, 2566, 3849, 5132, 6415, 7698, 12830, 15396, 19245, 25660, 38490, 76980.
What is 76980 in binary?
10010110010110100 (hexadecimal 12CB4, octal 226264).
What is the square root of 76980?
About 277.4527, exactly 2√19245.
Is 76980 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 76980?
76980 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.