The number 77000
77000 is a composite number with 64 divisors. Its prime factorisation is × × 7 × 11. Divisors (64): 1, 2, 4, 5, 7, 8, 10, 11, 14, 20, 22, 25, 28, 35, 40, 44 … 77000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77000: a Harshad number: divisible by its digit sum 14.
- 2
77000 is composite. Its prime factorisation is
- 3
The divisors add up to 224640; without 77000 itself that is 147640, so 77000 is abundant (147640 is more than 77000). Euler's totient φ(77000) = 24000 numbers up to 77000 share no factor with it.
- 4
The digits of 77000 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77000 = 2^{3} \times 5^{3} \times 7 \times 11 \]77000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 224640 |
| Euler totient φ(n) | 24000 |
| Square | 5929000000 |
| Cube | 456533000000000 |
| Square root | 277.488739 (= 10√770) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.7 × |
77000 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand |
| Binary (base 2) | 10010110011001000 |
| Octal (base 8) | 226310 |
| Hexadecimal (base 16) | 12CC8 |
| Base 3 | 10220121212 |
| As time | 77000 seconds = 21 h 23 min 20 s |
Is 77000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77000 ÷ 2 = 38500) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77000 ÷ 4 = 19250) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77000 ÷ 5 = 15400) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77000 ÷ 7 = 11000) | 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 | Yes (77000 ÷ 8 = 9625) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77000 ÷ 10 = 7700) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (77000 ÷ 11 = 7000) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77000 a prime number?
No. 77000 = × × 7 × 11, so it is divisible by 2.
What are the factors of 77000?
1, 2, 4, 5, 7, 8, 10, 11, 14, 20, 22, 25, 28, 35, 40, 44, 50, 55, 56, 70, 77, 88, 100, 110, 125, 140, 154, 175, 200, 220, 250, 275, 280, 308, 350, 385, 440, 500, 550, 616, 700, 770, 875, 1000, 1100, 1375, 1400, 1540, 1750, 1925, 2200, 2750, 3080, 3500, 3850, 5500, 7000, 7700, 9625, 11000, 15400, 19250, 38500, 77000.
What is 77000 in binary?
10010110011001000 (hexadecimal 12CC8, octal 226310).
What is the square root of 77000?
About 277.4887, exactly 10√770.
Is 77000 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 77000?
77000 is a Harshad number: divisible by its digit sum 14.