The number 77440
77440 is a composite number with 48 divisors. Its prime factorisation is × 5 × . Divisors (48): 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 64, 80 … 77440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77440: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 22.
- 2
77440 is composite. Its prime factorisation is
- 3
The divisors add up to 203490; without 77440 itself that is 126050, so 77440 is abundant (126050 is more than 77440). Euler's totient φ(77440) = 28160 numbers up to 77440 share no factor with it.
- 4
The digits of 77440 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77440 = 2^{7} \times 5 \times 11^{2} \]77440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 203490 |
| Euler totient φ(n) | 28160 |
| Square | 5996953600 |
| Cube | 464404086784000 |
| Square root | 278.280434 (= 88√10) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 24 |
| Scientific notation | 7.744 × |
77440 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand four hundred and forty |
| Binary (base 2) | 10010111010000000 |
| Octal (base 8) | 227200 |
| Hexadecimal (base 16) | 12E80 |
| Base 3 | 10221020011 |
| As time | 77440 seconds = 21 h 30 min 40 s |
Is 77440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77440 ÷ 2 = 38720) | 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 (77440 ÷ 4 = 19360) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77440 ÷ 5 = 15488) | 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 | No (remainder 6) | 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 (77440 ÷ 8 = 9680) | 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 (77440 ÷ 10 = 7744) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (77440 ÷ 11 = 7040) | 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 77440 a prime number?
No. 77440 = × 5 × , so it is divisible by 2.
What are the factors of 77440?
1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 64, 80, 88, 110, 121, 128, 160, 176, 220, 242, 320, 352, 440, 484, 605, 640, 704, 880, 968, 1210, 1408, 1760, 1936, 2420, 3520, 3872, 4840, 7040, 7744, 9680, 15488, 19360, 38720, 77440.
What is 77440 in binary?
10010111010000000 (hexadecimal 12E80, octal 227200).
What is the square root of 77440?
About 278.2804, exactly 88√10.
Is 77440 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 77440?
77440 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 22.