The number 13972
13972 is a composite number with 12 divisors. Its prime factorisation is × 7 × 499. Divisors (12): 1, 2, 4, 7, 14, 28, 499, 998, 1996, 3493, 6986, 13972.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13972 is composite. Its prime factorisation is
- 3
The divisors add up to 28000; without 13972 itself that is 14028, so 13972 is abundant (14028 is more than 13972). Euler's totient φ(13972) = 5976 numbers up to 13972 share no factor with it.
- 4
The digits of 13972 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13972 = 2^{2} \times 7 \times 499 \]13972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 28000 |
| Euler totient φ(n) | 5976 |
| Square | 195216784 |
| Cube | 2727568906048 |
| Square root | 118.203215 (= 2√3493) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3972 × |
13972 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and seventy-two |
| Binary (base 2) | 11011010010100 |
| Octal (base 8) | 33224 |
| Hexadecimal (base 16) | 3694 |
| Base 3 | 201011111 |
| As time | 13972 seconds = 3 h 52 min 52 s |
Is 13972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13972 ÷ 2 = 6986) | 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 (13972 ÷ 4 = 3493) | 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 (13972 ÷ 7 = 1996) | 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 4) | 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 2) | 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 13972 a prime number?
No. 13972 = × 7 × 499, so it is divisible by 2.
What are the factors of 13972?
1, 2, 4, 7, 14, 28, 499, 998, 1996, 3493, 6986, 13972.
What is 13972 in binary?
11011010010100 (hexadecimal 3694, octal 33224).
What is the square root of 13972?
About 118.2032, exactly 2√3493.
Is 13972 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 13972?
It is a composite number with 12 divisors.