The number 31440
31440 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 131. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 31440.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31440: a Harshad number: divisible by its digit sum 12.
- 2
31440 is composite. Its prime factorisation is
- 3
The divisors add up to 98208; without 31440 itself that is 66768, so 31440 is abundant (66768 is more than 31440). Euler's totient φ(31440) = 8320 numbers up to 31440 share no factor with it.
- 4
The digits of 31440 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 147 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31440 = 2^{4} \times 3 \times 5 \times 131 \]31440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 98208 |
| Euler totient φ(n) | 8320 |
| Square | 988473600 |
| Cube | 31077609984000 |
| Square root | 177.313282 (= 4√1965) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 147 |
| Scientific notation | 3.144 × |
31440 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand four hundred and forty |
| Binary (base 2) | 111101011010000 |
| Octal (base 8) | 75320 |
| Hexadecimal (base 16) | 7AD0 |
| Base 3 | 1121010110 |
| As time | 31440 seconds = 8 h 44 min 0 s |
Is 31440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31440 ÷ 2 = 15720) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31440 ÷ 3 = 10480) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31440 ÷ 4 = 7860) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31440 ÷ 5 = 6288) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31440 ÷ 6 = 5240) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | Yes (31440 ÷ 8 = 3930) | 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 | Yes (31440 ÷ 10 = 3144) | 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 | Yes (31440 ÷ 12 = 2620) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31440 a prime number?
No. 31440 = × 3 × 5 × 131, so it is divisible by 2.
What are the factors of 31440?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 131, 240, 262, 393, 524, 655, 786, 1048, 1310, 1572, 1965, 2096, 2620, 3144, 3930, 5240, 6288, 7860, 10480, 15720, 31440.
What is 31440 in binary?
111101011010000 (hexadecimal 7AD0, octal 75320).
What is the square root of 31440?
About 177.3133, exactly 4√1965.
Is 31440 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 31440?
31440 is a Harshad number: divisible by its digit sum 12.