The number 72624
72624 is a composite number with 40 divisors. Its prime factorisation is × 3 × 17 × 89. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 89, 102 … 72624.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72624: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
72624 is composite. Its prime factorisation is
- 3
The divisors add up to 200880; without 72624 itself that is 128256, so 72624 is abundant (128256 is more than 72624). Euler's totient φ(72624) = 22528 numbers up to 72624 share no factor with it.
- 4
The digits of 72624 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 187 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72624 = 2^{4} \times 3 \times 17 \times 89 \]72624 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 200880 |
| Euler totient φ(n) | 22528 |
| Square | 5274245376 |
| Cube | 383036796186624 |
| Square root | 269.488404 (= 4√4539) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 187 |
| Scientific notation | 7.2624 × |
72624 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand six hundred and twenty-four |
| Binary (base 2) | 10001101110110000 |
| Octal (base 8) | 215660 |
| Hexadecimal (base 16) | 11BB0 |
| Base 3 | 10200121210 |
| As time | 72624 seconds = 20 h 10 min 24 s |
Is 72624 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72624 ÷ 2 = 36312) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72624 ÷ 3 = 24208) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72624 ÷ 4 = 18156) | 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 (72624 ÷ 6 = 12104) | 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 (72624 ÷ 8 = 9078) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72624 ÷ 12 = 6052) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72624 a prime number?
No. 72624 = × 3 × 17 × 89, so it is divisible by 2.
What are the factors of 72624?
1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 89, 102, 136, 178, 204, 267, 272, 356, 408, 534, 712, 816, 1068, 1424, 1513, 2136, 3026, 4272, 4539, 6052, 9078, 12104, 18156, 24208, 36312, 72624.
What is 72624 in binary?
10001101110110000 (hexadecimal 11BB0, octal 215660).
What is the square root of 72624?
About 269.4884, exactly 4√4539.
Is 72624 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 72624?
72624 is a happy number: repeatedly adding the squares of its digits reaches 1.