The number 31980
31980 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 13 × 41. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 41, 52 … 31980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
31980 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
31980 is composite. Its prime factorisation is
- 3
The divisors add up to 98784; without 31980 itself that is 66804, so 31980 is abundant (66804 is more than 31980). Euler's totient φ(31980) = 7680 numbers up to 31980 share no factor with it.
- 4
The digits of 31980 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31980 = 2^{2} \times 3 \times 5 \times 13 \times 41 \]31980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 98784 |
| Euler totient φ(n) | 7680 |
| Square | 1022720400 |
| Cube | 32706598392000 |
| Square root | 178.829528 (= 2√7995) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.198 × |
31980 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand nine hundred and eighty |
| Binary (base 2) | 111110011101100 |
| Octal (base 8) | 76354 |
| Hexadecimal (base 16) | 7CEC |
| Base 3 | 1121212110 |
| As time | 31980 seconds = 8 h 53 min 0 s |
Is 31980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31980 ÷ 2 = 15990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31980 ÷ 3 = 10660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31980 ÷ 4 = 7995) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31980 ÷ 5 = 6396) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31980 ÷ 6 = 5330) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31980 ÷ 10 = 3198) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31980 ÷ 12 = 2665) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31980 a prime number?
No. 31980 = × 3 × 5 × 13 × 41, so it is divisible by 2.
What are the factors of 31980?
1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 41, 52, 60, 65, 78, 82, 123, 130, 156, 164, 195, 205, 246, 260, 390, 410, 492, 533, 615, 780, 820, 1066, 1230, 1599, 2132, 2460, 2665, 3198, 5330, 6396, 7995, 10660, 15990, 31980.
What is 31980 in binary?
111110011101100 (hexadecimal 7CEC, octal 76354).
What is the square root of 31980?
About 178.8295, exactly 2√7995.
Is 31980 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 31980?
It is a composite number with 48 divisors.