The number 72972
72972 is a composite number with 18 divisors. Its prime factorisation is × × 2027. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 2027, 4054, 6081, 8108, 12162, 18243, 24324 … 72972.
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How to work it out
- 1
72972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72972 is composite. Its prime factorisation is
- 3
The divisors add up to 184548; without 72972 itself that is 111576, so 72972 is abundant (111576 is more than 72972). Euler's totient φ(72972) = 24312 numbers up to 72972 share no factor with it.
- 4
The digits of 72972 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72972 = 2^{2} \times 3^{2} \times 2027 \]72972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 184548 |
| Euler totient φ(n) | 24312 |
| Square | 5324912784 |
| Cube | 388569535674048 |
| Square root | 270.133300 (= 6√2027) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 63 |
| Scientific notation | 7.2972 × |
72972 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand nine hundred and seventy-two |
| Binary (base 2) | 10001110100001100 |
| Octal (base 8) | 216414 |
| Hexadecimal (base 16) | 11D0C |
| Base 3 | 10201002200 |
| As time | 72972 seconds = 20 h 16 min 12 s |
Is 72972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72972 ÷ 2 = 36486) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72972 ÷ 3 = 24324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72972 ÷ 4 = 18243) | 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 (72972 ÷ 6 = 12162) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (72972 ÷ 9 = 8108) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72972 ÷ 12 = 6081) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72972 a prime number?
No. 72972 = × × 2027, so it is divisible by 2.
What are the factors of 72972?
1, 2, 3, 4, 6, 9, 12, 18, 36, 2027, 4054, 6081, 8108, 12162, 18243, 24324, 36486, 72972.
What is 72972 in binary?
10001110100001100 (hexadecimal 11D0C, octal 216414).
What is the square root of 72972?
About 270.1333, exactly 6√2027.
Is 72972 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 72972?
It is a composite number with 18 divisors.