The number 83972
83972 is a composite number with 12 divisors. Its prime factorisation is × 7 × 2999. Divisors (12): 1, 2, 4, 7, 14, 28, 2999, 5998, 11996, 20993, 41986, 83972.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
83972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
83972 is composite. Its prime factorisation is
- 3
The divisors add up to 168000; without 83972 itself that is 84028, so 83972 is abundant (84028 is more than 83972). Euler's totient φ(83972) = 35976 numbers up to 83972 share no factor with it.
- 4
The digits of 83972 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83972 = 2^{2} \times 7 \times 2999 \]83972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 168000 |
| Euler totient φ(n) | 35976 |
| Square | 7051296784 |
| Cube | 592111493546048 |
| Square root | 289.779226 (= 2√20993) |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 120 |
| Scientific notation | 8.3972 × |
83972 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand nine hundred and seventy-two |
| Binary (base 2) | 10100100000000100 |
| Octal (base 8) | 244004 |
| Hexadecimal (base 16) | 14804 |
| Base 3 | 11021012002 |
| As time | 83972 seconds = 23 h 19 min 32 s |
Is 83972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83972 ÷ 2 = 41986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83972 ÷ 4 = 20993) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (83972 ÷ 7 = 11996) | 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 2) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83972 a prime number?
No. 83972 = × 7 × 2999, so it is divisible by 2.
What are the factors of 83972?
1, 2, 4, 7, 14, 28, 2999, 5998, 11996, 20993, 41986, 83972.
What is 83972 in binary?
10100100000000100 (hexadecimal 14804, octal 244004).
What is the square root of 83972?
About 289.7792, exactly 2√20993.
Is 83972 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 83972?
It is a composite number with 12 divisors.