The number 972
972 is a composite number with 18 divisors. Its prime factorisation is × . Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324 … 972.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 972: a Harshad number: divisible by its digit sum 18.
- 2
972 is composite. Its prime factorisation is
- 3
The divisors add up to 2548; without 972 itself that is 1576, so 972 is abundant (1576 is more than 972). Euler's totient φ(972) = 324 numbers up to 972 share no factor with it.
- 4
The digits of 972 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 972 = 2^{2} \times 3^{5} \]972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 2548 |
| Euler totient φ(n) | 324 |
| Square | 944784 |
| Cube | 918330048 |
| Square root | 31.176915 (= 18√3) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 98 |
| Scientific notation | 9.72 × |
972 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and seventy-two |
| Roman numerals | CMLXXII |
| Binary (base 2) | 1111001100 |
| Octal (base 8) | 1714 |
| Hexadecimal (base 16) | 3CC |
| Base 3 | 1100000 |
| As time | 972 seconds = 16 min 12 s |
Is 972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (972 ÷ 2 = 486) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (972 ÷ 3 = 324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (972 ÷ 4 = 243) | 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 (972 ÷ 6 = 162) | 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 | Yes (972 ÷ 9 = 108) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (972 ÷ 12 = 81) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 972 a prime number?
No. 972 = × , so it is divisible by 2.
What are the factors of 972?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.
What is 972 in binary?
1111001100 (hexadecimal 3CC, octal 1714).
What is the square root of 972?
About 31.1769, exactly 18√3.
What is 972 in Roman numerals?
CMLXXII.
Is 972 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 972?
972 is a Harshad number: divisible by its digit sum 18.