The number 31724
31724 is a composite number with 24 divisors. Its prime factorisation is × 7 × 11 × 103. Divisors (24): 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 103, 154, 206, 308, 412, 721 … 31724.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31724: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
31724 is composite. Its prime factorisation is
- 3
The divisors add up to 69888; without 31724 itself that is 38164, so 31724 is abundant (38164 is more than 31724). Euler's totient φ(31724) = 12240 numbers up to 31724 share no factor with it.
- 4
The digits of 31724 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 77 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31724 = 2^{2} \times 7 \times 11 \times 103 \]31724 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 69888 |
| Euler totient φ(n) | 12240 |
| Square | 1006412176 |
| Cube | 31927419871424 |
| Square root | 178.112324 (= 2√7931) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 77 |
| Scientific notation | 3.1724 × |
31724 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand seven hundred and twenty-four |
| Binary (base 2) | 111101111101100 |
| Octal (base 8) | 75754 |
| Hexadecimal (base 16) | 7BEC |
| Base 3 | 1121111222 |
| As time | 31724 seconds = 8 h 48 min 44 s |
Is 31724 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31724 ÷ 2 = 15862) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31724 ÷ 4 = 7931) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (31724 ÷ 7 = 4532) | 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 8) | 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 | Yes (31724 ÷ 11 = 2884) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31724 a prime number?
No. 31724 = × 7 × 11 × 103, so it is divisible by 2.
What are the factors of 31724?
1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 103, 154, 206, 308, 412, 721, 1133, 1442, 2266, 2884, 4532, 7931, 15862, 31724.
What is 31724 in binary?
111101111101100 (hexadecimal 7BEC, octal 75754).
What is the square root of 31724?
About 178.1123, exactly 2√7931.
Is 31724 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 31724?
31724 is a happy number: repeatedly adding the squares of its digits reaches 1.