The number 32472
32472 is a composite number with 48 divisors. Its prime factorisation is × × 11 × 41. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 41, 44 … 32472.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32472: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
32472 is composite. Its prime factorisation is
- 3
The divisors add up to 98280; without 32472 itself that is 65808, so 32472 is abundant (65808 is more than 32472). Euler's totient φ(32472) = 9600 numbers up to 32472 share no factor with it.
- 4
The digits of 32472 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32472 = 2^{3} \times 3^{2} \times 11 \times 41 \]32472 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 98280 |
| Euler totient φ(n) | 9600 |
| Square | 1054430784 |
| Cube | 34239476418048 |
| Square root | 180.199889 (= 6√902) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 67 |
| Scientific notation | 3.2472 × |
32472 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand four hundred and seventy-two |
| Binary (base 2) | 111111011011000 |
| Octal (base 8) | 77330 |
| Hexadecimal (base 16) | 7ED8 |
| Base 3 | 1122112200 |
| As time | 32472 seconds = 9 h 1 min 12 s |
Is 32472 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32472 ÷ 2 = 16236) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32472 ÷ 3 = 10824) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32472 ÷ 4 = 8118) | 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 (32472 ÷ 6 = 5412) | 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 (32472 ÷ 8 = 4059) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32472 ÷ 9 = 3608) | 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 (32472 ÷ 11 = 2952) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (32472 ÷ 12 = 2706) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32472 a prime number?
No. 32472 = × × 11 × 41, so it is divisible by 2.
What are the factors of 32472?
1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 41, 44, 66, 72, 82, 88, 99, 123, 132, 164, 198, 246, 264, 328, 369, 396, 451, 492, 738, 792, 902, 984, 1353, 1476, 1804, 2706, 2952, 3608, 4059, 5412, 8118, 10824, 16236, 32472.
What is 32472 in binary?
111111011011000 (hexadecimal 7ED8, octal 77330).
What is the square root of 32472?
About 180.1999, exactly 6√902.
Is 32472 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 32472?
32472 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.