The number 45672
45672 is a composite number with 32 divisors. Its prime factorisation is × 3 × 11 × 173. Divisors (32): 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 173 … 45672.
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How to work it out
- 1
What is special about 45672: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.
- 2
45672 is composite. Its prime factorisation is
- 3
The divisors add up to 125280; without 45672 itself that is 79608, so 45672 is abundant (79608 is more than 45672). Euler's totient φ(45672) = 13760 numbers up to 45672 share no factor with it.
- 4
The digits of 45672 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 31 steps to reach 1.
LaTeX source of the formulas on this page
\[ 45672 = 2^{3} \times 3 \times 11 \times 173 \]45672 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 125280 |
| Euler totient φ(n) | 13760 |
| Square | 2085931584 |
| Cube | 95268667304448 |
| Square root | 213.710084 (= 2√11418) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 31 |
| Scientific notation | 4.5672 × |
45672 in other forms
| Form | Value |
|---|---|
| In words | forty-five thousand six hundred and seventy-two |
| Binary (base 2) | 1011001001101000 |
| Octal (base 8) | 131150 |
| Hexadecimal (base 16) | B268 |
| Base 3 | 2022122120 |
| As time | 45672 seconds = 12 h 41 min 12 s |
Is 45672 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (45672 ÷ 2 = 22836) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (45672 ÷ 3 = 15224) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (45672 ÷ 4 = 11418) | 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 (45672 ÷ 6 = 7612) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (45672 ÷ 8 = 5709) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | Yes (45672 ÷ 11 = 4152) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (45672 ÷ 12 = 3806) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 45672 a prime number?
No. 45672 = × 3 × 11 × 173, so it is divisible by 2.
What are the factors of 45672?
1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 173, 264, 346, 519, 692, 1038, 1384, 1903, 2076, 3806, 4152, 5709, 7612, 11418, 15224, 22836, 45672.
What is 45672 in binary?
1011001001101000 (hexadecimal B268, octal 131150).
What is the square root of 45672?
About 213.7101, exactly 2√11418.
Is 45672 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 45672?
45672 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.