The number 12972
12972 is a composite number with 24 divisors. Its prime factorisation is × 3 × 23 × 47. Divisors (24): 1, 2, 3, 4, 6, 12, 23, 46, 47, 69, 92, 94, 138, 141, 188, 276 … 12972.
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How to work it out
- 1
What is special about 12972: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
12972 is composite. Its prime factorisation is
- 3
The divisors add up to 32256; without 12972 itself that is 19284, so 12972 is abundant (19284 is more than 12972). Euler's totient φ(12972) = 4048 numbers up to 12972 share no factor with it.
- 4
The digits of 12972 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12972 = 2^{2} \times 3 \times 23 \times 47 \]12972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 32256 |
| Euler totient φ(n) | 4048 |
| Square | 168272784 |
| Cube | 2182834554048 |
| Square root | 113.894688 (= 2√3243) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.2972 × |
12972 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand nine hundred and seventy-two |
| Binary (base 2) | 11001010101100 |
| Octal (base 8) | 31254 |
| Hexadecimal (base 16) | 32AC |
| Base 3 | 122210110 |
| As time | 12972 seconds = 3 h 36 min 12 s |
Is 12972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12972 ÷ 2 = 6486) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12972 ÷ 3 = 4324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12972 ÷ 4 = 3243) | 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 (12972 ÷ 6 = 2162) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 3) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12972 ÷ 12 = 1081) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12972 a prime number?
No. 12972 = × 3 × 23 × 47, so it is divisible by 2.
What are the factors of 12972?
1, 2, 3, 4, 6, 12, 23, 46, 47, 69, 92, 94, 138, 141, 188, 276, 282, 564, 1081, 2162, 3243, 4324, 6486, 12972.
What is 12972 in binary?
11001010101100 (hexadecimal 32AC, octal 31254).
What is the square root of 12972?
About 113.8947, exactly 2√3243.
Is 12972 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 12972?
12972 is a happy number: repeatedly adding the squares of its digits reaches 1.