The number 31380
31380 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 523. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 523, 1046, 1569, 2092 … 31380.
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How to work it out
- 1
What is special about 31380: a Harshad number: divisible by its digit sum 15.
- 2
31380 is composite. Its prime factorisation is
- 3
The divisors add up to 88032; without 31380 itself that is 56652, so 31380 is abundant (56652 is more than 31380). Euler's totient φ(31380) = 8352 numbers up to 31380 share no factor with it.
- 4
The digits of 31380 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 178 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31380 = 2^{2} \times 3 \times 5 \times 523 \]31380 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 88032 |
| Euler totient φ(n) | 8352 |
| Square | 984704400 |
| Cube | 30900024072000 |
| Square root | 177.144009 (= 2√7845) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 178 |
| Scientific notation | 3.138 × |
31380 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand three hundred and eighty |
| Binary (base 2) | 111101010010100 |
| Octal (base 8) | 75224 |
| Hexadecimal (base 16) | 7A94 |
| Base 3 | 1121001020 |
| As time | 31380 seconds = 8 h 43 min 0 s |
Is 31380 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31380 ÷ 2 = 15690) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31380 ÷ 3 = 10460) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31380 ÷ 4 = 7845) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31380 ÷ 5 = 6276) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31380 ÷ 6 = 5230) | 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 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31380 ÷ 10 = 3138) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31380 ÷ 12 = 2615) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31380 a prime number?
No. 31380 = × 3 × 5 × 523, so it is divisible by 2.
What are the factors of 31380?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 523, 1046, 1569, 2092, 2615, 3138, 5230, 6276, 7845, 10460, 15690, 31380.
What is 31380 in binary?
111101010010100 (hexadecimal 7A94, octal 75224).
What is the square root of 31380?
About 177.1440, exactly 2√7845.
Is 31380 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 31380?
31380 is a Harshad number: divisible by its digit sum 15.