The number 72672
72672 is a composite number with 24 divisors. Its prime factorisation is × 3 × 757. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 757, 1514, 2271, 3028 … 72672.
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How to work it out
- 1
What is special about 72672: a Harshad number: divisible by its digit sum 24.
- 2
72672 is composite. Its prime factorisation is
- 3
The divisors add up to 191016; without 72672 itself that is 118344, so 72672 is abundant (118344 is more than 72672). Euler's totient φ(72672) = 24192 numbers up to 72672 share no factor with it.
- 4
The digits of 72672 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72672 = 2^{5} \times 3 \times 757 \]72672 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 191016 |
| Euler totient φ(n) | 24192 |
| Square | 5281219584 |
| Cube | 383796789608448 |
| Square root | 269.577447 (= 4√4542) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 68 |
| Scientific notation | 7.2672 × |
72672 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand six hundred and seventy-two |
| Binary (base 2) | 10001101111100000 |
| Octal (base 8) | 215740 |
| Hexadecimal (base 16) | 11BE0 |
| Base 3 | 10200200120 |
| As time | 72672 seconds = 20 h 11 min 12 s |
Is 72672 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72672 ÷ 2 = 36336) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72672 ÷ 3 = 24224) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72672 ÷ 4 = 18168) | 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 (72672 ÷ 6 = 12112) | 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 (72672 ÷ 8 = 9084) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72672 ÷ 12 = 6056) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72672 a prime number?
No. 72672 = × 3 × 757, so it is divisible by 2.
What are the factors of 72672?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 757, 1514, 2271, 3028, 4542, 6056, 9084, 12112, 18168, 24224, 36336, 72672.
What is 72672 in binary?
10001101111100000 (hexadecimal 11BE0, octal 215740).
What is the square root of 72672?
About 269.5774, exactly 4√4542.
Is 72672 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 72672?
72672 is a Harshad number: divisible by its digit sum 24.