The number 77344
77344 is a composite number with 12 divisors. Its prime factorisation is × 2417. Divisors (12): 1, 2, 4, 8, 16, 32, 2417, 4834, 9668, 19336, 38672, 77344.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77344: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77344 is composite. Its prime factorisation is
- 3
The divisors add up to 152334; without 77344 itself that is 74990, so 77344 is deficient (74990 is less than 77344). Euler's totient φ(77344) = 38656 numbers up to 77344 share no factor with it.
- 4
The digits of 77344 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77344 = 2^{5} \times 2417 \]77344 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 152334 |
| Euler totient φ(n) | 38656 |
| Square | 5982094336 |
| Cube | 462679104323584 |
| Square root | 278.107893 (= 4√4834) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 24 |
| Scientific notation | 7.7344 × |
77344 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand three hundred and forty-four |
| Binary (base 2) | 10010111000100000 |
| Octal (base 8) | 227040 |
| Hexadecimal (base 16) | 12E20 |
| Base 3 | 10221002121 |
| As time | 77344 seconds = 21 h 29 min 4 s |
Is 77344 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77344 ÷ 2 = 38672) | 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 (77344 ÷ 4 = 19336) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | 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 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 | Yes (77344 ÷ 8 = 9668) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | 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 77344 a prime number?
No. 77344 = × 2417, so it is divisible by 2.
What are the factors of 77344?
1, 2, 4, 8, 16, 32, 2417, 4834, 9668, 19336, 38672, 77344.
What is 77344 in binary?
10010111000100000 (hexadecimal 12E20, octal 227040).
What is the square root of 77344?
About 278.1079, exactly 4√4834.
Is 77344 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 77344?
77344 is a happy number: repeatedly adding the squares of its digits reaches 1.