The number 77472
77472 is a composite number with 36 divisors. Its prime factorisation is × × 269. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 77472.
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How to work it out
- 1
What is special about 77472: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77472 is composite. Its prime factorisation is
- 3
The divisors add up to 221130; without 77472 itself that is 143658, so 77472 is abundant (143658 is more than 77472). Euler's totient φ(77472) = 25728 numbers up to 77472 share no factor with it.
- 4
The digits of 77472 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77472 = 2^{5} \times 3^{2} \times 269 \]77472 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 221130 |
| Euler totient φ(n) | 25728 |
| Square | 6001910784 |
| Cube | 464980032258048 |
| Square root | 278.337924 (= 12√538) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 24 |
| Scientific notation | 7.7472 × |
77472 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand four hundred and seventy-two |
| Binary (base 2) | 10010111010100000 |
| Octal (base 8) | 227240 |
| Hexadecimal (base 16) | 12EA0 |
| Base 3 | 10221021100 |
| As time | 77472 seconds = 21 h 31 min 12 s |
Is 77472 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77472 ÷ 2 = 38736) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77472 ÷ 3 = 25824) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77472 ÷ 4 = 19368) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77472 ÷ 6 = 12912) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (77472 ÷ 8 = 9684) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77472 ÷ 9 = 8608) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77472 ÷ 12 = 6456) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77472 a prime number?
No. 77472 = × × 269, so it is divisible by 2.
What are the factors of 77472?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 269, 288, 538, 807, 1076, 1614, 2152, 2421, 3228, 4304, 4842, 6456, 8608, 9684, 12912, 19368, 25824, 38736, 77472.
What is 77472 in binary?
10010111010100000 (hexadecimal 12EA0, octal 227240).
What is the square root of 77472?
About 278.3379, exactly 12√538.
Is 77472 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 77472?
77472 is a happy number: repeatedly adding the squares of its digits reaches 1.