The number 72252
72252 is a composite number with 30 divisors. Its prime factorisation is × × 223. Divisors (30): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 223, 324 … 72252.
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How to work it out
- 1
What is special about 72252: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
72252 is composite. Its prime factorisation is
- 3
The divisors add up to 189728; without 72252 itself that is 117476, so 72252 is abundant (117476 is more than 72252). Euler's totient φ(72252) = 23976 numbers up to 72252 share no factor with it.
- 4
The digits of 72252 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 187 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72252 = 2^{2} \times 3^{4} \times 223 \]72252 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 189728 |
| Euler totient φ(n) | 23976 |
| Square | 5220351504 |
| Cube | 377180836867008 |
| Square root | 268.797321 (= 18√223) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 187 |
| Scientific notation | 7.2252 × |
72252 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand two hundred and fifty-two |
| Binary (base 2) | 10001101000111100 |
| Octal (base 8) | 215074 |
| Hexadecimal (base 16) | 11A3C |
| Base 3 | 10200010000 |
| As time | 72252 seconds = 20 h 4 min 12 s |
Is 72252 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72252 ÷ 2 = 36126) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72252 ÷ 3 = 24084) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72252 ÷ 4 = 18063) | 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 (72252 ÷ 6 = 12042) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72252 ÷ 9 = 8028) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72252 ÷ 12 = 6021) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72252 a prime number?
No. 72252 = × × 223, so it is divisible by 2.
What are the factors of 72252?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 223, 324, 446, 669, 892, 1338, 2007, 2676, 4014, 6021, 8028, 12042, 18063, 24084, 36126, 72252.
What is 72252 in binary?
10001101000111100 (hexadecimal 11A3C, octal 215074).
What is the square root of 72252?
About 268.7973, exactly 18√223.
Is 72252 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72252?
72252 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.