The number 72988
72988 is a composite number with 12 divisors. Its prime factorisation is × 71 × 257. Divisors (12): 1, 2, 4, 71, 142, 257, 284, 514, 1028, 18247, 36494, 72988.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72988: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
72988 is composite. Its prime factorisation is
- 3
The divisors add up to 130032; without 72988 itself that is 57044, so 72988 is deficient (57044 is less than 72988). Euler's totient φ(72988) = 35840 numbers up to 72988 share no factor with it.
- 4
The digits of 72988 add up to 34, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 187 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72988 = 2^{2} \times 71 \times 257 \]72988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 130032 |
| Euler totient φ(n) | 35840 |
| Square | 5327248144 |
| Cube | 388825187534272 |
| Square root | 270.162914 (= 2√18247) |
| Digit sum / digital root | 34 / 7 |
| Collatz steps to 1 | 187 |
| Scientific notation | 7.2988 × |
72988 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand nine hundred and eighty-eight |
| Binary (base 2) | 10001110100011100 |
| Octal (base 8) | 216434 |
| Hexadecimal (base 16) | 11D1C |
| Base 3 | 10201010021 |
| As time | 72988 seconds = 20 h 16 min 28 s |
Is 72988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72988 ÷ 2 = 36494) | 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 (72988 ÷ 4 = 18247) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72988 a prime number?
No. 72988 = × 71 × 257, so it is divisible by 2.
What are the factors of 72988?
1, 2, 4, 71, 142, 257, 284, 514, 1028, 18247, 36494, 72988.
What is 72988 in binary?
10001110100011100 (hexadecimal 11D1C, octal 216434).
What is the square root of 72988?
About 270.1629, exactly 2√18247.
Is 72988 divisible by 3?
No. Its digits add up to 34, which is not a multiple of 3.
What is special about the number 72988?
72988 is a happy number: repeatedly adding the squares of its digits reaches 1.