The number 72264
72264 is a composite number with 16 divisors. Its prime factorisation is × 3 × 3011. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 3011, 6022, 9033, 12044, 18066, 24088, 36132, 72264.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72264: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
72264 is composite. Its prime factorisation is
- 3
The divisors add up to 180720; without 72264 itself that is 108456, so 72264 is abundant (108456 is more than 72264). Euler's totient φ(72264) = 24080 numbers up to 72264 share no factor with it.
- 4
The digits of 72264 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72264 = 2^{3} \times 3 \times 3011 \]72264 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 180720 |
| Euler totient φ(n) | 24080 |
| Square | 5222085696 |
| Cube | 377368800735744 |
| Square root | 268.819642 (= 2√18066) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.2264 × |
72264 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand two hundred and sixty-four |
| Binary (base 2) | 10001101001001000 |
| Octal (base 8) | 215110 |
| Hexadecimal (base 16) | 11A48 |
| Base 3 | 10200010110 |
| As time | 72264 seconds = 20 h 4 min 24 s |
Is 72264 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72264 ÷ 2 = 36132) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72264 ÷ 3 = 24088) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72264 ÷ 4 = 18066) | 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 | Yes (72264 ÷ 6 = 12044) | 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 (72264 ÷ 8 = 9033) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72264 ÷ 12 = 6022) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72264 a prime number?
No. 72264 = × 3 × 3011, so it is divisible by 2.
What are the factors of 72264?
1, 2, 3, 4, 6, 8, 12, 24, 3011, 6022, 9033, 12044, 18066, 24088, 36132, 72264.
What is 72264 in binary?
10001101001001000 (hexadecimal 11A48, octal 215110).
What is the square root of 72264?
About 268.8196, exactly 2√18066.
Is 72264 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 72264?
72264 is a happy number: repeatedly adding the squares of its digits reaches 1.