The number 77376
77376 is a composite number with 56 divisors. Its prime factorisation is × 3 × 13 × 31. Divisors (56): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 31, 32, 39, 48, 52 … 77376.
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How to work it out
- 1
What is special about 77376: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77376 is composite. Its prime factorisation is
- 3
The divisors add up to 227584; without 77376 itself that is 150208, so 77376 is abundant (150208 is more than 77376). Euler's totient φ(77376) = 23040 numbers up to 77376 share no factor with it.
- 4
The digits of 77376 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 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77376 = 2^{6} \times 3 \times 13 \times 31 \]77376 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 227584 |
| Euler totient φ(n) | 23040 |
| Square | 5987045376 |
| Cube | 463253623013376 |
| Square root | 278.165418 (= 8√1209) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 63 |
| Scientific notation | 7.7376 × |
77376 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand three hundred and seventy-six |
| Binary (base 2) | 10010111001000000 |
| Octal (base 8) | 227100 |
| Hexadecimal (base 16) | 12E40 |
| Base 3 | 10221010210 |
| As time | 77376 seconds = 21 h 29 min 36 s |
Is 77376 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77376 ÷ 2 = 38688) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77376 ÷ 3 = 25792) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77376 ÷ 4 = 19344) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77376 ÷ 6 = 12896) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (77376 ÷ 8 = 9672) | 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 | No (remainder 6) | 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 (77376 ÷ 12 = 6448) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77376 a prime number?
No. 77376 = × 3 × 13 × 31, so it is divisible by 2.
What are the factors of 77376?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 31, 32, 39, 48, 52, 62, 64, 78, 93, 96, 104, 124, 156, 186, 192, 208, 248, 312, 372, 403, 416, 496, 624, 744, 806, 832, 992, 1209, 1248, 1488, 1612, 1984, 2418, 2496, 2976, 3224, 4836, 5952, 6448, 9672, 12896, 19344, 25792, 38688, 77376.
What is 77376 in binary?
10010111001000000 (hexadecimal 12E40, octal 227100).
What is the square root of 77376?
About 278.1654, exactly 8√1209.
Is 77376 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 77376?
77376 is a happy number: repeatedly adding the squares of its digits reaches 1.