The number 72504
72504 is a composite number with 48 divisors. Its prime factorisation is × × 19 × 53. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 36, 38, 53, 57, 72 … 72504.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72504: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
72504 is composite. Its prime factorisation is
- 3
The divisors add up to 210600; without 72504 itself that is 138096, so 72504 is abundant (138096 is more than 72504). Euler's totient φ(72504) = 22464 numbers up to 72504 share no factor with it.
- 4
The digits of 72504 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 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72504 = 2^{3} \times 3^{2} \times 19 \times 53 \]72504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 210600 |
| Euler totient φ(n) | 22464 |
| Square | 5256830016 |
| Cube | 381141203480064 |
| Square root | 269.265668 (= 6√2014) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 94 |
| Scientific notation | 7.2504 × |
72504 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand five hundred and four |
| Binary (base 2) | 10001101100111000 |
| Octal (base 8) | 215470 |
| Hexadecimal (base 16) | 11B38 |
| Base 3 | 10200110100 |
| As time | 72504 seconds = 20 h 8 min 24 s |
Is 72504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72504 ÷ 2 = 36252) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72504 ÷ 3 = 24168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72504 ÷ 4 = 18126) | 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 (72504 ÷ 6 = 12084) | 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 | Yes (72504 ÷ 8 = 9063) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72504 ÷ 9 = 8056) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72504 ÷ 12 = 6042) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72504 a prime number?
No. 72504 = × × 19 × 53, so it is divisible by 2.
What are the factors of 72504?
1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 36, 38, 53, 57, 72, 76, 106, 114, 152, 159, 171, 212, 228, 318, 342, 424, 456, 477, 636, 684, 954, 1007, 1272, 1368, 1908, 2014, 3021, 3816, 4028, 6042, 8056, 9063, 12084, 18126, 24168, 36252, 72504.
What is 72504 in binary?
10001101100111000 (hexadecimal 11B38, octal 215470).
What is the square root of 72504?
About 269.2657, exactly 6√2014.
Is 72504 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72504?
72504 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.