The number 77980
77980 is a composite number with 24 divisors. Its prime factorisation is × 5 × 7 × 557. Divisors (24): 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 557, 1114, 2228, 2785 … 77980.
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How to work it out
- 1
77980 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77980 is composite. Its prime factorisation is
- 3
The divisors add up to 187488; without 77980 itself that is 109508, so 77980 is abundant (109508 is more than 77980). Euler's totient φ(77980) = 26688 numbers up to 77980 share no factor with it.
- 4
The digits of 77980 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77980 = 2^{2} \times 5 \times 7 \times 557 \]77980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 187488 |
| Euler totient φ(n) | 26688 |
| Square | 6080880400 |
| Cube | 474187053592000 |
| Square root | 279.248993 (= 2√19495) |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.798 × |
77980 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and eighty |
| Binary (base 2) | 10011000010011100 |
| Octal (base 8) | 230234 |
| Hexadecimal (base 16) | 1309C |
| Base 3 | 10221222011 |
| As time | 77980 seconds = 21 h 39 min 40 s |
Is 77980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77980 ÷ 2 = 38990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77980 ÷ 4 = 19495) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77980 ÷ 5 = 15596) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77980 ÷ 7 = 11140) | 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 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77980 ÷ 10 = 7798) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77980 a prime number?
No. 77980 = × 5 × 7 × 557, so it is divisible by 2.
What are the factors of 77980?
1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 557, 1114, 2228, 2785, 3899, 5570, 7798, 11140, 15596, 19495, 38990, 77980.
What is 77980 in binary?
10011000010011100 (hexadecimal 1309C, octal 230234).
What is the square root of 77980?
About 279.2490, exactly 2√19495.
Is 77980 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 77980?
It is a composite number with 24 divisors.