The number 72352
72352 is a composite number with 48 divisors. Its prime factorisation is × 7 × 17 × 19. Divisors (48): 1, 2, 4, 7, 8, 14, 16, 17, 19, 28, 32, 34, 38, 56, 68, 76 … 72352.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72352: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 19.
- 2
72352 is composite. Its prime factorisation is
- 3
The divisors add up to 181440; without 72352 itself that is 109088, so 72352 is abundant (109088 is more than 72352). Euler's totient φ(72352) = 27648 numbers up to 72352 share no factor with it.
- 4
The digits of 72352 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72352 = 2^{5} \times 7 \times 17 \times 19 \]72352 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 181440 |
| Euler totient φ(n) | 27648 |
| Square | 5234811904 |
| Cube | 378749110878208 |
| Square root | 268.983271 (= 4√4522) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 24 |
| Scientific notation | 7.2352 × |
72352 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand three hundred and fifty-two |
| Binary (base 2) | 10001101010100000 |
| Octal (base 8) | 215240 |
| Hexadecimal (base 16) | 11AA0 |
| Base 3 | 10200020201 |
| As time | 72352 seconds = 20 h 5 min 52 s |
Is 72352 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72352 ÷ 2 = 36176) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72352 ÷ 4 = 18088) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (72352 ÷ 7 = 10336) | 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 (72352 ÷ 8 = 9044) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72352 a prime number?
No. 72352 = × 7 × 17 × 19, so it is divisible by 2.
What are the factors of 72352?
1, 2, 4, 7, 8, 14, 16, 17, 19, 28, 32, 34, 38, 56, 68, 76, 112, 119, 133, 136, 152, 224, 238, 266, 272, 304, 323, 476, 532, 544, 608, 646, 952, 1064, 1292, 1904, 2128, 2261, 2584, 3808, 4256, 4522, 5168, 9044, 10336, 18088, 36176, 72352.
What is 72352 in binary?
10001101010100000 (hexadecimal 11AA0, octal 215240).
What is the square root of 72352?
About 268.9833, exactly 4√4522.
Is 72352 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 72352?
72352 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 19.