The number 9972
9972 is a composite number with 18 divisors. Its prime factorisation is × × 277. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324 … 9972.
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How to work it out
- 1
9972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9972 is composite. Its prime factorisation is
- 3
The divisors add up to 25298; without 9972 itself that is 15326, so 9972 is abundant (15326 is more than 9972). Euler's totient φ(9972) = 3312 numbers up to 9972 share no factor with it.
- 4
The digits of 9972 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 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9972 = 2^{2} \times 3^{2} \times 277 \]9972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 25298 |
| Euler totient φ(n) | 3312 |
| Square | 99440784 |
| Cube | 991623498048 |
| Square root | 99.859902 (= 6√277) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 135 |
| Scientific notation | 9.972 × |
9972 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and seventy-two |
| Binary (base 2) | 10011011110100 |
| Octal (base 8) | 23364 |
| Hexadecimal (base 16) | 26F4 |
| Base 3 | 111200100 |
| As time | 9972 seconds = 2 h 46 min 12 s |
Is 9972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9972 ÷ 2 = 4986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9972 ÷ 3 = 3324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9972 ÷ 4 = 2493) | 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 (9972 ÷ 6 = 1662) | 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 (9972 ÷ 9 = 1108) | 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 (9972 ÷ 12 = 831) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9972 a prime number?
No. 9972 = × × 277, so it is divisible by 2.
What are the factors of 9972?
1, 2, 3, 4, 6, 9, 12, 18, 36, 277, 554, 831, 1108, 1662, 2493, 3324, 4986, 9972.
What is 9972 in binary?
10011011110100 (hexadecimal 26F4, octal 23364).
What is the square root of 9972?
About 99.8599, exactly 6√277.
Is 9972 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9972?
It is a composite number with 18 divisors.