The number 21972
21972 is a composite number with 12 divisors. Its prime factorisation is × 3 × 1831. Divisors (12): 1, 2, 3, 4, 6, 12, 1831, 3662, 5493, 7324, 10986, 21972.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21972: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
21972 is composite. Its prime factorisation is
- 3
The divisors add up to 51296; without 21972 itself that is 29324, so 21972 is abundant (29324 is more than 21972). Euler's totient φ(21972) = 7320 numbers up to 21972 share no factor with it.
- 4
The digits of 21972 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 131 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21972 = 2^{2} \times 3 \times 1831 \]21972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 51296 |
| Euler totient φ(n) | 7320 |
| Square | 482768784 |
| Cube | 10607395722048 |
| Square root | 148.229552 (= 2√5493) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 131 |
| Scientific notation | 2.1972 × |
21972 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand nine hundred and seventy-two |
| Binary (base 2) | 101010111010100 |
| Octal (base 8) | 52724 |
| Hexadecimal (base 16) | 55D4 |
| Base 3 | 1010010210 |
| As time | 21972 seconds = 6 h 6 min 12 s |
Is 21972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21972 ÷ 2 = 10986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21972 ÷ 3 = 7324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21972 ÷ 4 = 5493) | 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 (21972 ÷ 6 = 3662) | 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 | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21972 ÷ 12 = 1831) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21972 a prime number?
No. 21972 = × 3 × 1831, so it is divisible by 2.
What are the factors of 21972?
1, 2, 3, 4, 6, 12, 1831, 3662, 5493, 7324, 10986, 21972.
What is 21972 in binary?
101010111010100 (hexadecimal 55D4, octal 52724).
What is the square root of 21972?
About 148.2296, exactly 2√5493.
Is 21972 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 21972?
21972 is a happy number: repeatedly adding the squares of its digits reaches 1.