The number 97972
97972 is a composite number with 12 divisors. Its prime factorisation is × 7 × 3499. Divisors (12): 1, 2, 4, 7, 14, 28, 3499, 6998, 13996, 24493, 48986, 97972.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
97972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
97972 is composite. Its prime factorisation is
- 3
The divisors add up to 196000; without 97972 itself that is 98028, so 97972 is abundant (98028 is more than 97972). Euler's totient φ(97972) = 41976 numbers up to 97972 share no factor with it.
- 4
The digits of 97972 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 190 steps to reach 1.
LaTeX source of the formulas on this page
\[ 97972 = 2^{2} \times 7 \times 3499 \]97972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 196000 |
| Euler totient φ(n) | 41976 |
| Square | 9598512784 |
| Cube | 940385494474048 |
| Square root | 313.004792 (= 2√24493) |
| Digit sum / digital root | 34 / 7 |
| Collatz steps to 1 | 190 |
| Scientific notation | 9.7972 × |
97972 in other forms
| Form | Value |
|---|---|
| In words | ninety-seven thousand nine hundred and seventy-two |
| Binary (base 2) | 10111111010110100 |
| Octal (base 8) | 277264 |
| Hexadecimal (base 16) | 17EB4 |
| Base 3 | 11222101121 |
| As time | 97972 seconds = 27 h 12 min 52 s |
Is 97972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (97972 ÷ 2 = 48986) | 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 (97972 ÷ 4 = 24493) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (97972 ÷ 7 = 13996) | 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 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 97972 a prime number?
No. 97972 = × 7 × 3499, so it is divisible by 2.
What are the factors of 97972?
1, 2, 4, 7, 14, 28, 3499, 6998, 13996, 24493, 48986, 97972.
What is 97972 in binary?
10111111010110100 (hexadecimal 17EB4, octal 277264).
What is the square root of 97972?
About 313.0048, exactly 2√24493.
Is 97972 divisible by 3?
No. Its digits add up to 34, which is not a multiple of 3.
What is special about the number 97972?
It is a composite number with 12 divisors.