The number 13974
13974 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 17 × 137. Divisors (16): 1, 2, 3, 6, 17, 34, 51, 102, 137, 274, 411, 822, 2329, 4658, 6987, 13974.
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How to work it out
- 1
13974 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13974 is composite. Its prime factorisation is
- 3
The divisors add up to 29808; without 13974 itself that is 15834, so 13974 is abundant (15834 is more than 13974). Euler's totient φ(13974) = 4352 numbers up to 13974 share no factor with it.
- 4
The digits of 13974 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13974 = 2 \times 3 \times 17 \times 137 \]
13974 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 29808 |
| Euler totient φ(n) | 4352 |
| Square | 195272676 |
| Cube | 2728740374424 |
| Square root | 118.211675 |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3974 × |
13974 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and seventy-four |
| Binary (base 2) | 11011010010110 |
| Octal (base 8) | 33226 |
| Hexadecimal (base 16) | 3696 |
| Base 3 | 201011120 |
| As time | 13974 seconds = 3 h 52 min 54 s |
Is 13974 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13974 ÷ 2 = 6987) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13974 ÷ 3 = 4658) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13974 ÷ 6 = 2329) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13974 a prime number?
No. 13974 = 2 × 3 × 17 × 137, so it is divisible by 2.
What are the factors of 13974?
1, 2, 3, 6, 17, 34, 51, 102, 137, 274, 411, 822, 2329, 4658, 6987, 13974.
What is 13974 in binary?
11011010010110 (hexadecimal 3696, octal 33226).
What is the square root of 13974?
About 118.2117.
Is 13974 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 13974?
It is a composite number with 16 divisors.